Here in the USA operating under Part 121, any twin-engined airliner that has to shutdown an engine must land at the nearest suitable airport in point-of-time. It doesn't matter whether the airline has service at that "nearest" airport. If they don't, they use the maintenance folks from other airlines (or FBOs) that may be there. If there is none, they'll send put their own mechanics and tools on another airline's flight, and deal with it when they arrive. Most airlines will help each other out in these cases (when they don't serve the diversion city) since what comes around goes around, and next time the situation could be reversed.
ALL views, opinions expressed are mine ONLY and are NOT representative of those shared by Southwest Airlines Co.