I don't believe that it is compressed. We did try compacting it, and the locks still hung on through that. It actually took a restart of that computer to wipe out the locks.
I found out some more information on file geodatabases, that explains some of my problem. Apparently with file geodatabases, if someone is viewing the data (has it open on their map), and then another user goes in to edit, it will not allow them to save edits, since they cannot acquire a lock. But if that person is editing the data first, and then others open it to view it, it works fine. So it comes down to who gets into the data first.
I do not have an explanation for why the locks do not go away when people close out of the program. The locks hang on sometimes until that person restarts their computer. Like I said before, they even hang on through a compaction. This happens pretty inconsistently, sometimes the locks hang on and sometimes they don't. I still don't understand this.