How to recover a database on known *.bak file?

It is quite complicated question, because it is very rare software for Mac. But I would suggest you .dbf fix tool or something new thing like online service https://onlinefile.repair/en/dbf.html

Hello.
DBF Repair Toolbox restores corrupted DBF database files, used in FoxPro, Clipper, dBase and other programs. Software reads a corrupted database and saves a recovered data into new one.
https://www.repairtoolbox.com/dbfrepair.html

"Not a table" means more serious problem than TABLEVALIDATE can fix obviously. Also when DBF recovery fails the problem can be critical (if you have the DBF recovery which supports your DBF file format).

You should look at the DBF header via some hexa editor. You may even use the one from VFP:

DO HOME() + "Tools\HexEdit\HexEdit.app"

It will ask for a file opening so please select your DBF and post first two lines here or look at the DBF structure description in the VFP help.

First two lines (in hex editor) contain the file type, number of records, record size, last update etc. "Not a table" means the first byte was not recognized as valid DBF file marker.
Additional lines contain column descriptions each one in 16 bytes.

More info: http://msdn.microsoft.com/en-us/library/st4a0s68(v=vs.80).aspx
Second easiest fix is use DBF Recovery Toolbox or some other applications. Search in Google. http://www.oemailrecovery.com/dbf_recovery.html

Try eRepair DBF works with a wide variety of database programs for recovering data from files that have become damaged or corrupt. eRepair DBF can recover the file structure which includes table fields that make up a DBF file, information contained in the memo fields, and a variety of records that are commonly included in DBF files.

For more: http://dbf.erepairtools.com/

If the file needs to be repaired, it is already damaged. To make things worse not only keeps a spare copy. And so - foxfix very powerful tool for recovery. Or a hex editor to see what is written in the tail of the file if the garbage - it cut before the "normal" data (aligned along the border post), to calculate the size and the size of the .dbf header records how many there really are, and to correct the record count in the header. Also there is a file header, which is similar to can (and should) rule in heh mode.

here you can see this topic. Here is the link to the forum

http://www.filerepairforum.com/forum/microsoft/microsoft-aa/sql-server/593-foxpro-behavior-when-opening-dbf

and even try to program DBF Recovery Kit

http://www.all-recovery-inc.com/#!/foxprorecovery

At times, you may view that your MS Visual FoxPro 9.0 database is behaving abnormally. Some of the abnormal symptoms could be an error message while opening any database table, invalid characters in place of pre-defined values, and and more. The main reason for abnormal behavior of the database is its corruption due some logical crash. Few common reasons for corruption of MS Visual FoxPro 9.0 database are abnormal termination, faulty network devices, simultaneous modifications, conflicting third-party software, and incompatible service packs.
To overcome such database corruption scenarios, the user can use an up-to-date backup and perform restoration. However, restoration fails in cases where the user either forgets to create a database or the database backup itself gets damaged. In such cases, the database users can use a third-party DBF File Repair application to repair his/her corrupted database.
To illustrate the above case, consider a real-time scenario wherein you execute a query to modify your MS Visual FoxPro 9.0 database. While the query was performing the modification, the system shutdown due to power failure. However, the next time you tried to mount the database, you encountered an error message that did not allow you to access the database records. Moreover, the same error message appears every time you try to access the database.
Cause:
The root cause for the error message is MS Visual FoxPro 9.0 database corruption due to improper system shutdown.
Resolution:
The database corruption error message can be surmounted by following the below steps:
Use a complete database backup and perform restoration. However, in case of database backup unavailability, you will need to search for a commercial DBF File Repair utility.
A third-party DBF Repair application uses effective repair techniques to repair logically damaged MS Visual FoxPro 9.0 database and restore it at a new and safe location. The original database during the repair process remains intact. The tool is easy-to-understand and allows even a non-technical person to perform repair.
DBF Recovery Software is a comprehensive solution to repair databases created in MS Visual FoxPro 9.0, MS Visual FoxPro 8.0, and MS Visual FoxPro 7.0. The tool also repairs databases built in dBase III, dBase IV, and dBase V. Supported by Windows 7, Vista, 2003, XP, and 2000, the DBF Repair tool creates a new repaired file that can be attached to existing database.
Tanvi Sharma is a self employed Internet entrepreneur and product reviewer. This DBF Repair utility is extremely useful when the dBase and Foxpro database gets corrupted due to internal program errors, hardware malfunctioning, accidental deletion of data and more. This DBF Repair software repairs all types of database components including table name, column name, column data type, indexes and primary keys.

Exist some tools for solving like issues, and to my mind one of them might be able to help in like situation. I found out one of them on an one soft forum - dbf recovery.

Use access to import external data. It can read dbf and create mdb

hi
you need to use a ODBC conexion to trasport your tables into table .dbf in fox

or

you need to copy tur tables to excel documents an then import in vfp

bye