This kind of happens to me too...but the freezing on closing happens when my Capture Device (LGP) freezes for the session...and causes OBS Studio to freeze when attempting to close...and keeps a process in the background just like you described.
I circumvented the issue of my LGP randomly freezing for the rest of the session by upgrading my graphics drivers, but it seems to have only worked for my Windows 10 partition, and not for my Windows 7 (even after upgrading my graphics drivers with the same drivers) partition which I would prefer to use for streaming as it doesn't use as many resources in the background as Windows 10.
There's one bug that remains with the LGP on my side of things, when you deactivate the feed on properties...it stays frozen/deactivated when you try to re-activate, then the problem with the OBS freezing on 'close' happens.
So I have to avoid at all cost on touching any 'settings/properties options' on my capture device, and if the sound gets all cracking on me, I just have to unplug the HDMI and plug back in?
Do you recognize this issue
@Jim by any chance? Could the Browser plugin be causing these issues as well?