This happened to my state's library system a while back. Public computers and free wifi were down for a few months, but no major disruptions of lending services. I don't think the state paid any ransom, instead they just repaired their systems.

Since we are talking about e-borrowing I assume DRM are involved. If they are not, ignore the rest.

The point of DRM (ignoring their terrible side effect) is precisely to keep on controlling data even after content has been released. There is a validation mechanism (typically pinging back the digital right owner) to insure that the file can indeed be read. So... do not validate all the signed books already out, issue a new key for the library to "e-borrow" (hate that term) once again. Why is this even taking more than 1min? I don't get it. It feels like once again in theory it could be positive but in practice the negative side effects of DRMs trump out everything.

Wipe the system and start again.

Today, it could probably disappear and no one would miss it. There's a reason these places operate on a shoestring budget and haven't bothered to update software security. The services we value, we pay for or vote for. If there was a proposition to close libraries in favor of some other minor benefit (e.g. one extra field trip for every school child per year), it would probably lose badly.

Probably most of the relevant functions of a library can be accomplished by other more efficient means. Student loan forgiveness (librarians), homeless shelters with computers, and free daycare for kids. That's basically what people use it for now, and all can be better done if we just admit what its for and do that instead.