How would this work in the event of your membership running out; does the library cease to work or do you keep it? And how does one stop one person from downloading it and then sharing the code with their friends, completely making buying it pointless?

I don't think either point matters too much. Nothing stops me from downloading a song on itunes and giving it to everyone (except the law). Same thing with a lot of other software and computer games, for example.

At any rate, its a great way to drum up a little extra cash flow at little to no expense of BYOND (they could probably implement this in an hour?)

To answer your questions more specifically:
1. Yes, you just get it if you're a member. If your membership runs out, well you can't get it again but you can keep it on your hard drive. You're only entitled to updates if you're an active member when the update comes out.

2. Nothing stops you from giving it to your friends, and honestly I don't think it matters much in this situation. It just gives a little more incentive to be a member, "Access to membership-only libraries!"

You didn't read what I said, I said make it an option to library authors. Not all libraries are members only. Its only specific libraries that authors want to specify as members only.