I know in Europe that troops got lost from there units on occasion and usually when they found another unit they just reported in. Usually they were just told to join a squad and the LT or Captain in charge would just report back to the rear he found so-and-so and drafted him into his unit. I remember reading about this happening a lot in the early days of France and during the Battle of the Bulge. Including one gent who ended up serving in several different units over a three week period and finally ended up in a artillery company for the rest of the war.
As for the Twilight War there is no rear anymore and once the 'your on your own speech' happens there really is no US Military anymore either but for what the troops make for themselves. The Generals won't just leave after all but try to hold things together for as long as they can. So probably they will keep things together and attempt to use military justice with deserters on a case by case basis. Either shooting definite deserters or putting them in with other units as replacements.
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