Many .gdb and .dbf files exists and most of them are some sort of database, so this conversion in vast majority of cases represents just a transformation of one database format to another. There is no exact answer for this conversion as individual programs may support only particular file types that all share the same extension, but generally speaking, this conversion should be possible.
If you need help with some exact gdb to dbf conversion between two special database types, your best option would be to consult support or dedicated forums for your database software.