| Looking at your profile you don't list what gear you have so helping you is a little bit harder. However since Fender type basses are the most common, I'm going to venture you have a Fender or Fender copy of some sort.
Fender.com has a stringing guide, you're supposed to trim each string at a certain length for each post.
Trimming the wire end short on a flatwound string poses two risks. Firstly if the wire is too short, you risk the thick part of the string being wrapped around the tuning post. For rounds this isn't as much of a problem but for flats its a death sentence. When you tune up, and they're wrapped around the post, they can snap easily.
The second problem is, is the inherent tension of flatwound strings. When you don't trim the strings to their right length, the tension of pulling on less wire. This means that the wire on top of the string is more prone to snap while you're playing and thusly screwing you out of a string.
I've never seen anything but the cheapest flatwounds unwinding. But like any string if you put too much tension on it, they can break. The weakest part of the string is the skinny little section by the headstock so they usually break there. However they can also break by the bridge, like any other string. When they snap sometimes they unravel, but either way your string is shot.
Flatwounds are awesome strings and most of my basses are strung with them. If you're unsure about how to set up a bass for flats, take it into a tech. Not only for trimming the strings but for setting the action and intonation as well since you're most likely using a different gauge and they have more tension.
Hope this helps.
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