Well, I have never had a string break on the bridge... The ones I have had break have been above my neck pickup...
However, I see what you are talking about.
Keep in mind, there are 3 types of strings that you are referring to.
#1 - Exposed Core Strings: An example of Exposed Core Strings are LaBella Super Steps / Fodera Anthony Jackson Sigs / SIT Power Core. These have no winding at all over the core where the core passes over the bridge.
#2 - Exposed Core with Very Thin Wrap Wire around the core wire: An example of these would be GHS Contact Cores / MTD Exposed Core B's. These are still considered "Exposed Core" but they do have a very thin wire around them that would prevent them from slinging out if they broke where the core is "exposed."
#3 - Taper Core Strings. These have a taper over the bridge section that is wrapped with less windings over this taper section. Not as thin as an exposed core, but not as thick as a full wound string. These I do not see having that issue you are afraid of at all.
Now, with all of that said, I do not know how either of them will really react if the core broke over the bridge section, but I would guess that #3 Taper Core would be less dramatic, while #1 would be the most. I do know that you do not want a .020 Plain Steel string snapping on you while you are playing it. I am glad to not have experienced that but maybe I should give it a shot with one
I mainly have used Taper Core strings (#3), although I have been wanting to try Exposed Cores (#1) on some of my basses.
I do know some people who use style #1 on some crazy custom through body have to route the exposed section through basically a guitar bridge w/ extreme bends and has never had one broken... soooo, I wouldnt really worry about it... (unless you leave the strings on getting totally rusted, then I wouldnt play it)