If a participant has a FSA carryover, but quits before they have used their funds, is that money then forfeited? Or will the terminated participant still have a run-out period to submit receipts for date-of-service up to their termination date?

If year-to-date contributions exceed the amount of reimbursements and there is a remaining balance, the employee has a COBRA election available for the remainder of the plan year. If they do not elect COBRA, then expenses can only be submitted up to the end of their termination run-out period after which and funds remaining would be forfeited.