One sometimes hears of planes with many passengers holding third world passports having issues when they must divert. IIRC there was a case at CDG with a plane to India. Most passengers from India had already used single entry EU visas and were not permitted to enter again for an overnight stay while the aircraft was being repaired. As a result, anyone who could enter the EU was sent to a hotel at the airline's expense and the rest--mostly Asians--were forced to spend the night in the terminal.

Sometimes the airline can arrange for some sort of emergency exception to visa rules, but this seems to depend on not only the country where the diversion happens and what their regulations are in these cases but also on the airline's relationship with local authorities and how willing they are to be flexible.

I was on a flight AMS-MSP that did a medical diversion to Canada. What was interesting was that the ill passenger was from South Africa and did not have a visa to enter Canada. Nevertheless she was taken to a hospital in Canada. Her luggage was offloaded too, but it may have been held in bond until she was able to leave Canada rather than being taken through customs without her.