Since the current answers skim over what I think is the key point I'm going to add a late answer.
The risk is that the fender itself can jam a wheel. If a front wheel jams you're almost certainly going to crash, with a rear wheel you might crash.
Good fenders will have a means for every stay to pull away from the bike relatively easily, so that if somehow the fender dos get hooked onto the wheel the fender gets destroyed and the bike keeps rolling.
Bad designs are typically a metal rod bolted to the bike at one end and the fender at the other. They usually look like this:
The problem is that if that stay catches on the wheel it will pivot around to some point then jam, stopping the wheel from rotating. You'll note that those are two different images - these days it's less common to find this design precisely because it is dangerous. Sheldon Brown has an exmaple
The easy solution is to use a clamp on one end of each stay, like these:
You won't see a single fender with those at both ends (that would be silly), but they should have a clamp at one end. Always.
One thing I advise to to buy fenders where the clamping parts don't fall off when the stay is pulled out. Those on the left above, for example, will lose the end cap and the bolt if the stay pulls out. Finding a small bolt on a dark road is often hard, and while you can usually buy replacements it's annoying. I currently have one bike where the fender is only loosely attacked because I caught the fender on something while wrestling it out of a crowded bicycle park, and couldn't find one of the bolts afterwards. $3 for a replacement bolt, but $10 for postage since no-one locally stocks that particular spare part.