F1 visa student with unpaid hospital bills

The social security administration does not keep records of unpaid debts. There is no immigration law on the subject of credit reports.

The unpaid hospital bills would go onto your credit report rating. It is unlikely immigration authorities would find out about these. That being said, please do your best to comply with your financial obligations because when some people don't pay bills - or at least make payment plans - it makes payments increase for everyone else to absorb the loss. Also, being financially irresponsible could potentially cause immigration consequences (among other consequences) depending on your future plans in this country. If you have an emergency necessity, you may be able to obtain a work permit even as an F1 so you can start paying off the bills.

This is not an immigration question.