He has a current US Passport and an expired Polish passport.
Sorry but he legally must use his Polish passport for entering and leaving Poland. It is a crime for him to identify himself to any Polish government official with documents other than Polish ones. The good news is that he can legally use an expired Polish passport to enter Poland (although he'll need his valid US passport to get onto the plane). The bad news is that he can't leave Poland on an expired passport.
Similar to U.S. laws that require U.S. citizens to enter and exit on a valid U.S. passport, Poland also requires Polish citizens (including dual U.S. citizens or those with claims to Polish citizenship) to enter and depart Poland using a Polish passport. If you are a U.S. citizen and also a Polish citizen, or if you are unsure if you hold Polish citizenship, you should contact the nearest Polish consular office for further information.