Most airlines will have basic plans in place on how to deal with passenger welfare at diversion airports along their flight path. However, most "situations" that occur during these diversions are due to exception processing (eg. refugee/stateless travel documents, etc...) or authorities failing to exercise effective discretion (eg. denying entry to otherwise inadmissable passengers when the regulations permit entry to be exceptionally granted under certain conditions). In well over 99% of cases, there are no issues for passengers affected by en route international diversions.

That said, the only country that conducts checks on passengers overflying their airspace is the United States. Passengers whose names appear on selected US Government compiled lists may not fly on aircraft that either enter US airspace or that come within a specific radius of US airspace.