You are able to file for benefits from your Ex spouse IF you were married for at least 10 years, AND you did not remarry.
You mentioned that you no longer had his SS#, so you would need to provide his place and date of birth as well as his parents’ names.
If you don't have this information also, you will need to contact your local SSA office and see if there is anything else that they would accept to prove your claim.
You mention that your ex still owed you back child support. You may be able to receive benefits for your child if they are under age 18, or permanently disabled.
Please see below:
Unfortunately, if you do not qualify for the above survivor's benefits, then there is no way to recoup any back child support from your ex unless you can file a claim against his estate. (If you think you may qualify, please see an attorney)
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