Are you referring to the OP's kids (if she had any) or the girlfriend's ?

Re nibbs.......I'm assuming (which of course had made a you know what of of me before !) that if she didn't leave him until the 37 year mark, any kids nibbs had with him are probably grown by now.

Re the girlfriend's......yes, they would be eligible for the family benefit under nibb's (possibly, stbx) husband, IF he gets SSDI. He just has to name them as his children with the SSA. It doesn't matter to the SSA that the kids were born out of wedlock. They only care about where to send the payments (which is accounts in the kid's names) and info about their benefits (which would go to their legal custodian....in this case, all in the same household)