I've found a couple snake baskets on islands. Whether they randomly spawned there or were simply left by players I couldn't tell you. But they definitely don't show up nearly as often as pig crates or chicken coops, and even those are far too rare to be of much use.
We need a way of purchasing baskets, crates and coops when we've lost ours for whatever reason. It's rather silly not to be able to complete a merchant voyage because nobody will give us another cage.
Also, right click should release a caged animal. I have on occasion caught the wrong type of chicken when chasing one in the dark, or in a pack of chickens. Then what? Since you can't get another coop, you're done.