Which is exactly why he needs to insist that he is just transiting the airport to Ukraine.
He doesn't need to insist on anything. He needs to follow the signs in Chopin for airside transit. He should be able to arrange a ticket there for onwards travel without entering Poland or even attempting to do so. In Europe, we don't have to pass through immigration and customs control upon landing, we can stay airside. As long as he has a ticket for onwards travel for today or tomorrow, it's fine.
She can meet him in Lwow and experience its overwhelming Polish culture.
More likely, she can meet him there and realise that it's very much the beating heart of Ukrainian nationalism these days.
If asked about the overstay, he might just say that he had problem leaving over the holidays.
Doesn't work. Schengen rules are very rigid, and if you find yourself in that situation, you are supposed to go to the border police before the overstay occurs so that they can register it. It's a strict liability offence and no defence exists for overstaying without previously documented evidence.
If he doesn't look like a dirtball or a terrorist, and is polite, they might cut him a break and not put him on a black list.
They have no discretion. He has overstayed, therefore he has committed an offence.