Although DaveB provided all the extensions, but I think you might be looking for something a little more specific to the data and tables.
In VFP, if you have a database container, you can do it a few ways... have a database located in one folder/path, and the actual TABLES in another path... Not anything I would recommend, but that MAY be what you are encountering. The database will have the path where the tables are EXPECTED to be found when you try to open them.
The other is to have both the database AND the tables in the same folder. There are 3 files for the database itself
.dbc -- database
.dcx -- compound index of database
.dct -- memo field content for database
Additionally, the tables can have up to 3 files each with respective suffixes
.dbf -- single table
.cdx -- compound index for the single table
.fpt -- memo field content for the single table
So, if you have moved the tables from one location to another and they don't have same paths in expected location, that will cause you some headaches. If you have VFP, you can open the database as a table and browse it to see what is expected where. For example
CD Whatever\Your\DataPathIs
use NameOfYourDatabase.dbc (yes, explicitly add the .dbc suffix)
browse for objectType = "Table"
then, if you double-click the "memo" field column for the property, you'll see a bunch of non-viewable characters represented by square boxes and then a path that corresponds to where the database is EXPECTING to find the file.
This might be the missing piece you are looking for.