PersonVUE app keep detecting the apps that are closed.

Give this a try: boot into Safe Mode according to How to use safe mode on your Mac and try to run PersonVUE from there. Reboot normally and test again.

NOTE 1: Safe Mode boot can take up to 3 - 5 minutes as it's doing the following; 

• Verifies your startup disk and attempts to repair directory issues, if needed

• Loads only required kernel extensions (prevents 3rd party kernel/extensions from loading)

• Prevents Startup Items and Login Items from opening automatically

• Disables user-installed fonts 

• Deletes font caches, kernel cache, and other system cache files

NOTE 2: if you have a wireless keyboard with rechargeable batteries connect it with its charging cable before booting into Safe Mode. This makes it act as a wired keyboard as will insure a successful boot into Safe Mode.

If it runs successfully in Safe Mode but not in normal mode maybe you can take the test from Safe Mode.

Have you installed and run any "cleaning", "optimizing", "speed-up", anti-virus or VPN apps on your Mac?

We are not Apple, cannot speak for Apple and cannot intervene on your behalf with Apple. We're just volunteers here and end users like you.

PersonVUE is not an Apple product and as such the developer is responsible for making it work with macOS. If you have problems with the app you need to talk to the app's tech support. Or possibly inquire in a PersonVUE user forum. I can't imagine a developer refusing support requests, but then I'm seldom surprised any more.

Of course a person familiar with your issue may come along here, but one may not.