What happens to an unclaimed patient with amnesia?

For instance a person who has been brought into a hospital with an head injury that leaves them unconscious. They awaken with normal memories of day to day actions (eating, zippers, etc) but no memory of themself. If no one claims them and their memory is not recovered, after physical therapy, does social services step in to assist in a new life?What happens to an unclaimed patient with amnesia?
This counts as traumatic brain injury, which is a disability. The disability services from that state and social security disability would step in at that point, I believe.What happens to an unclaimed patient with amnesia?
The social services unit at the hospital would be involved from the beginning, notifying the police and taking other necessary legal action. If the person's memory was not recovered, they would assist in locating appropriate living arrangements, legal guardians, etc. through available community services. Such a case would be so rare as to be non-existent in reality. Most people have fingerprints on file somewhere, have items in their possession which would give clues to their identity, and publicity, in this day of the 24 hour news cycle, would be extensive leading to the likelihood of someone identifying the person quickly. it would also be extremely rare for an individual to recover no memories at all.