Back Child Support and SSI?

My daughter's father hasn't been in her life for years. The courts ordered him to pay $165 a month, but he couldn't keep a job for whatever excuse he wants to give. I have been disabled myself since 2010 and I receive a check for her as well. Her father smoked like a chimney and ended up with COPD and congestive heart failure. Now he has to be on oxygen 24/7 and is applying for disability. I understand that there are 2 kinds, SSI (for those who haven't earned enough through working) and SSDI (for those who have worked a legitimate job and made money over the table.) Unfortunately her father worked a lot of "under the table" jobs so I doubt he will qualify for SSDI. I've heard that if he gets the SSI, all of his back child support (he owes roughly $10,000) will be forgiven. Please someone tell me I'm wrong! That would be so unfair to the children of these deadbeat dads!