Assuming you are closed shop (I think all alpa carriers are) they can petition the company to fire you for non-payment. It might take a while, but it can be done.

Not sure if I'd string them along over $200 since it's hard to predict how long your termination will take. I suspect that you would get a certified-mail warning before they fire you.

Another option is to resign from the union...legally you can do that but you still must pay some or all of the dues for your representation, even as a non-member. You are correct in that they don't care if you are a member, but they do care about your dues...enough to fire you.

Unions in this industry are a damned-if-you-do, damned-if-you-don't proposition.