How would you remove him from office then?
He is the highest officer in the land. SCOTUS does not have a national police force. Remember when President Andrew Jackson directly disobeyed a ruling of the Supremes with veritable impunity. Obama would have to order his own Attorney General to have himself removed from office.
Or would Biden suddenly knock on Obama's door and and say, "sorry Barry, it's been fun but you should not be here." "Hugs to Michelle and the kids." "I'll see you next time I fly AF-1 into ChiTown."
It's just pipedreams.
Historically, the U.S. Marshals Service has taken responsibility for serving most Federal court criminal process. However, the courts have become more receptive to other law enforcement personnel serving criminal proces
However if a court should declare him to be ineligible, and the ruling is not overturned, I don't expect their will be any shortage of people willing to "help" him leave. Probably to include some of his own protective detail.