Just to be clear, that's much different then just making a run for it and wanting to fly out with nothing. He would have substitute documentation, even if it was not technically a passport.
Now, at least for the USA, if you just show up at the border and claim citizenship I'm sure you can get in, even if you have to claim asylum. They just detain you until your citizenship is verified. Like a social security number, drivers license, passport record, whatever, but you have to make it to the border somehow. Everything is cross checked including pictures and fingerprints.
One option would be to hire passage on a sea vessel via the black market or hire a boat (or even buy a vessel) and just take off. Then proclaim citizenship when intercepted by the coast guard in home country waters.