You can still file. Enter all zeros for the parent SSN. The parent won’t be able to get an FSA ID, so you will need to follow the instructions for sending the signature page by mail. Report the amount of money they earned.
If they actually do have an SSN but don’t earn enough money that they have to file a tax return, you just report the amount they made. Aid officers are used to seeing low income on the FAFSA, so don’t worry about that.