It is a proprietary Microsoft format created by Foxpro. That doesn't mean other producers don't use the same extension for files of a different format, which clouds the issue quite a lot. (And frustrates Foxpro users, who thinnk they have a Foxpro file but don't.) For one of my desktop apps I chose "rms" for the extension, which is actually a Realplayer extension. Oops.dbf was sort of just a generic database file
From the description of the behavior, though, it sounds like your files are Foxpro. Did you look on Ebay for someone selling an older version of that program?