If you mean parents using their children SSN to open a credit card, this is because US banking system is always decades behind the rest of the world, so they just accept the number blindly even though technically the children aren't allowed to open a loan yet, being minor.

In theory once the child grows up and shocked that their credit score is ruined, they can file a police report to wipe the debt, but that also means their parents will go to jail, a large risk considering they're likely not in a good physical/mental health in the first place.

Other countries solved this by either having national ID or a working KYC system.

It is possible to defraud a lender and cause your own child grief from bad credit reports and creditors but ultimately the debt isn't collectible or lawful as should be obvious.