>If the whole world flooded a small library with library card requests, etc. while being funded by a small community, there is probably a good chance that library won't last.

What would actually happen in that scenario, assuming that the people running the library are the tiniest bit competent, is that the library would stop making library cards available to non-residents.

No library is going to start offering a service, see it quickly draining their resources, and just watch as their budget is run into the ground.