I am sure many companies are like what you described. We are the same way. In the past I don't get notified most of the time when someone leaves for whatever reason.
When I find out then I will log in as that user and review what they have. If I have any questions then I send the supervisor an email asking them what to do with them. Sometimes they will have me just delete them all and other times they will have one of their other users check the files.
I will also make sure there are no workspaces left for any upgrade. I created a report that lets me know who has workspaces and the files in them.
However, recently our HR department began sending out a termination email every friday to everyone. The termination could be for any reason though. That gives me the names to check in windchill if they were there.