I have a 7 years old son and his biological father has played no part in his life my husband of 7 years has raised him, a few days ago my sons biological father contacted me through Facebook and said he wants to sign over his right. My question is if he signs over his right does he still have to pay the 16,000 dollars of back child support?

Yes, back support is not "erased" by your husband adopting your child. Unless your husband adopts, by the way, your "ex" can't relinquish his rights.

Ongoing support would stop. Past-due support is still owing.

Of course, whether you try to collect the arrearages is your choice.

An adoption requires an Attorney so this is one of those things you could cover with him/her - waive or not waive past-due support.

Also you could let the debt pass if he does sign adoption papers. One problem I see here is that you haven't said if your husband approves of an adoption. Also by the title you haven't described any situation that implies your ex to be a deadbat dad.

You refer to $16K in back support. Was there a court order for support?