如何跟踪窗口关闭点击

我不太明白你的问题是什么，试试这个：

from PyQt5 import QtCore, QtGui, QtWidgets


class DialogArchName(QtWidgets.QDialog):
    def __init__(self, parent=None):
        super(DialogArchName, self).__init__(parent)
        
        self.namef = ''
        self.pathf = ''
        
        label = QtWidgets.QLabel("Введите имя архива:")
        self.namefield = QtWidgets.QLineEdit()
        btnchoice = QtWidgets.QPushButton('Выбрать путь', clicked=self.getpath)
        self.rar_arch = QtWidgets.QRadioButton('.rar')
        self.zip_arch = QtWidgets.QRadioButton('.zip')
        btnOk = QtWidgets.QPushButton("Архивировать", clicked=self.getname)
        
        layout = QtWidgets.QGridLayout(self)
        layout.addWidget(label, 0, 0, 1, 1)
        layout.addWidget(self.rar_arch, 0, 1, 1, 1)
        
        layout.addWidget(self.namefield, 1, 0, 1, 1)
        layout.addWidget(self.zip_arch, 1, 1, 1, 1)
        
        layout.addWidget(btnchoice, 3, 0, 1, 1)       # высота, право
        layout.addWidget(btnOk, 3, 1, 1, 1)
        
# ???    def closeEvent(self, a0: QtWidgets.QDialog.closeEvent) -> None:
# ???        QtWidgets.QDialog.closeEvent()
    def closeEvent(self, event):
        reply = QtWidgets.QMessageBox.question(
            self, 
            'Информация',
            'Вы уверены, что хотите закрыть Dialog?',
             QtWidgets.QMessageBox.Yes,
             QtWidgets.QMessageBox.No)
        if reply == QtWidgets.QMessageBox.Yes:
            # тут делайте что вам надо перед закрытием диалога
            event.accept()
        else:
            event.ignore()


    def getname(self):
        self.namef = self.namefield.text()
# ???        self.hide()
# ???        return self.namef

    def getpath(self):
        self.pathf = QtWidgets.QFileDialog.getExistingDirectory()
        
# ???        return self.pathf
        
        
if __name__ == "__main__":
    import sys
    app = QtWidgets.QApplication(sys.argv)
    w = DialogArchName()
    w.show()
    sys.exit(app.exec_())        

更新：

尽管您解释得不好，但我对您的任务的理解是这样的：

主文件

...
class ExampleApp(QtWidgets.QMainWindow, front.Ui_MainWindow):
...


# архивация 
    def arch(self):                                                # архивация
        dirfiles = []
        if self.pathFile == '':
            if self.directory == '':
                QtWidgets.QMessageBox.information(None, 'Ошибка', 'Выберите папку либо файл')
                return # +++
            else:
                path = Path(self.directory)
                dirfiles = [str(f.absolute()) for f in path.glob("**/*")]
        else:
            pass
  
        if dirfiles:
            self.dialogname.exec_()
            
            dialogname = self.dialogname.namef
            pathname = self.dialogname.pathf
            
            if dialogname:
                if pathname:
                    archive_name = pathname+'/'+dialogname
                else:
                    archive_name = dialogname
            else:
                if pathname:
                    archive_name = pathname + '/' + os.path.split(self.directory)[-1]
                else:
                    archive_name = os.path.split(self.directory)[-1]

# !!! +++
            if self.dialogname.close_forcibly:                             # !!! +++
                QtWidgets.QMessageBox.information(                         # !!! +++
                    self,                                                  # !!! +++
                    'Ошибка',                                              # !!! +++
                    'Что-то пошло не так'                                  # !!! +++
                )                                                          # !!! +++
                return                                                     # !!! +++
            
            try:
                shutil.make_archive(archive_name, 'zip', path)
                #print(self.closeEvent(QtWidgets.QDialog.closeEvent))
                QtWidgets.QMessageBox.information(None, 'Успех', 'Архивирование успешно завершено')
            except Exception:
                print(traceback.format_exc())
                QtWidgets.QMessageBox.information(None, 'Ошибка', 'Что-то пошло не так')
 
        if self.pathFile:
            print(self.pathFile)
            self.dialogname.exec_()
            dialogname = self.dialogname.namef
            pathname = self.dialogname.pathf
            if dialogname:
                if pathname:
                    archive = zipfile.ZipFile(pathname+'/'+dialogname+'.zip', 'w')
                else:
                    archive = zipfile.ZipFile(dialogname + '.zip', 'w')
            else:
                if pathname:
                    archive = zipfile.ZipFile(pathname+'/'+os.path.split(self.pathFile[0])[-1] + '.zip', 'w')
                else:
                    archive = zipfile.ZipFile(os.path.split(self.pathFile[0])[-1] + '.zip', 'w')
            try:
                for i in self.pathFile:
                    try:
                        archive.write(i, arcname=os.path.split(i)[-1], compress_type=zipfile.ZIP_DEFLATED)
                    except Exception:
                        print(traceback.format_exc())
            except Exception:
                QtWidgets.QMessageBox.information(None, 'Ошибка', 'Что-то пошло не так')
            else:
                QtWidgets.QMessageBox.information(None, 'Успех', 'Архивирование успешно завершено')
            archive.close()
 
...

前台.py

from PyQt5 import QtCore, QtGui, QtWidgets, Qt
 
 
class Ui_MainWindow():
    def setupUi(self, MainWindow):
        MainWindow.setObjectName("MainWindow")
        MainWindow.resize(300, 250)
        MainWindow.setMinimumSize(QtCore.QSize(500, 230))
        MainWindow.setMaximumSize(QtCore.QSize(500, 230))
        MainWindow.setAutoFillBackground(False)
        self.centralwidget = QtWidgets.QWidget(MainWindow)
        self.centralwidget.setObjectName("centralwidget")
        self.btnBrowse = QtWidgets.QPushButton(self.centralwidget)
        self.btnBrowse.setGeometry(QtCore.QRect(10, 0, 221, 23))
        self.btnBrowse.setObjectName("btnBrowse")
        self.listWidget = QtWidgets.QListWidget(self.centralwidget)
        self.listWidget.setGeometry(QtCore.QRect(10, 30, 221, 151))
        self.listWidget.setObjectName("listWidget")
        self.btnArch = QtWidgets.QPushButton(self.centralwidget)
        self.btnArch.setGeometry(QtCore.QRect(10, 185, 221, 23))
        self.btnArch.setObjectName("btnArch")
        self.browseArch = QtWidgets.QPushButton(self.centralwidget)
        self.browseArch.setGeometry(QtCore.QRect(260, 0, 221, 23))
        self.browseArch.setObjectName("browseArch")
        self.exlist = QtWidgets.QListWidget(self.centralwidget)
        self.exlist.setGeometry(QtCore.QRect(260, 30, 221, 151))
        self.exlist.setObjectName("exlist")
        self.exButton = QtWidgets.QPushButton(self.centralwidget)
        self.exButton.setGeometry(QtCore.QRect(260, 185, 221, 23))
        self.exButton.setObjectName("exButton")
        MainWindow.setCentralWidget(self.centralwidget)
 
        self.retranslateUi(MainWindow)
        QtCore.QMetaObject.connectSlotsByName(MainWindow)
 
    def retranslateUi(self, MainWindow):
        _translate = QtCore.QCoreApplication.translate
        MainWindow.setWindowTitle(_translate("MainWindow", "Archivator"))
        self.btnBrowse.setText(_translate("MainWindow", "Выбрать..."))
        self.btnArch.setText(_translate("MainWindow", "Архивировать"))
        self.browseArch.setText(_translate("MainWindow", "Выбрать архив"))
        self.exButton.setText(_translate("MainWindow", "Извлечь"))
 
 
class Dialog(QtWidgets.QDialog):                                                   
    def __init__(self, parent=None):
        super(Dialog, self).__init__(parent)
 
        label = QtWidgets.QLabel("Выберите:")
        self.rbDir = QtWidgets.QRadioButton('Папку', self)
        self.rbPath = QtWidgets.QRadioButton('Файлы', self)
        btnOk = QtWidgets.QPushButton("Ok", clicked=self.hide)
        layout = QtWidgets.QGridLayout(self)
        layout.addWidget(label, 0, 0, 1, 3)
        layout.addWidget(self.rbDir, 1, 1, 1, 1)
        layout.addWidget(self.rbPath, 2, 1, 1, 1)
        layout.addWidget(btnOk, 3, 2, 1, 1)
 
 
class DialogArchName(QtWidgets.QDialog):
    def __init__(self, parent=None):
        super(DialogArchName, self).__init__(parent)
        
        self.namef = ''
        self.pathf = ''
# +++
        self.close_forcibly = False                                             # +++
        
        label = QtWidgets.QLabel("Введите имя архива:")
        self.namefield = QtWidgets.QLineEdit()
        btnchoice = QtWidgets.QPushButton('Выбрать путь', clicked=self.getpath)
        self.rar_arch = QtWidgets.QRadioButton('.rar')
        self.zip_arch = QtWidgets.QRadioButton('.zip')
        btnOk = QtWidgets.QPushButton("Архивировать", clicked=self.getname)
        layout = QtWidgets.QGridLayout(self)
        layout.addWidget(btnchoice, 3, 1, 1, 1)  # высота, право
        layout.addWidget(label, 0, 0, 1, 3)
        layout.addWidget(self.namefield, 1, 1, 1, 1)
        layout.addWidget(self.rar_arch, 0, 2, 3, 3)
        layout.addWidget(self.zip_arch, 1, 2, 3, 3)
        layout.addWidget(btnOk, 3, 2, 1, 1)
 
    def closeEvent(self, a0: QtWidgets.QDialog.closeEvent) -> None:
# ???        QtWidgets.QDialog.closeEvent(self, a0)
# +++
        self.close_forcibly = True                                    # +++
 
    def getname(self):
        self.namef = self.namefield.text()
# +++
        self.close_forcibly = False                                   # +++
        
        self.hide()                           
  
# ???        return self.namef
 
    def getpath(self):
        self.pathf = QtWidgets.QFileDialog.getExistingDirectory()
# ???        return self.pathf