Usually its the lower link that fails, so it just dangles for a while... I guess if the upper one goes, then it is likely to get broken off.
I noticed that the front right one was dangling from the top on the Impreza at the end of winter, but I think it had been broken for months without me knowing it. The link is short though and I couldn't see it getting jammed on anything important, so I waited until it was convenient. Having the sway bar back in action did make a noticeable difference, and now on a couple of bumpy corners it quit bottoming out the outside front suspension.