My ex-wife passed away and her mother filed her taxes but she owed back child support. How does that work? who will receive the refund

I'm very sorry for your loss.

She may if she filed her late daughter's tax return.  However, the back child support may cause an offset (i.e., if your late ex-wife has already been reported to the Bureau of the Fiscal Service (BFS), the IRS and/or state's Department of Revenue may take all or part of her refund if she was due one).

For more information: https://fiscal.treasury.gov/top/