It kind of sounds like some sort of unhandled deadlock where two or more systems are waiting for access to something the other is using.

Often a suspect for this is an ID tabel or the like that stores primary keys as many parts of the application may require use of it to do some update or another. Archiving tables are also another possible culprit.

Slow networks or too much trafic can contribute to it by widening the frame of time that resources are locked and thus increasing the chance of conflict. The fact that when one user killed thier app the others were able to continue also supports this kind of issue. I don't personaly have a lot of experience with this on foxpro tables but more wtih SQL server.