Anything unfastened is open or unbuttoned. If your dog frequently escapes through an unfastened gate in your backyard, you might want to buy a more secure latch.
When something is fastened, it's locked, hooked, tied, or otherwise secured. So when you undo whatever is securing it, it's unfastened. An unfastened seatbelt is a recipe for disaster, but an unfastened necktie or belt buckle can make you much more comfortable. If you have an unfastened clasp on your suspenders, your pants might fall down. (How embarrassing!)