I think the OP might mean a possible string (say, for instance, a very long URI... anything without spaces or hyphens I think it will happen) that will push past the boundary of the container.
I've come across this problem a couple of times, sometimes the solution isn't really so much a solution as it is a workaround.
Would it be practical (or even possible) to put a fixed-width table inside the floated div in order to contain text?
I don't think that will work for long, unbroken strings.
Sometimes people who quote long lines of code etc. have this problem - they usually just automatically overflow so there's a horizontal scrollbar - or I've known one or two sites where the unbroken string was forcibly broken after a set amount of characters (via PHP.)
Is this your problem, and are those suitable solutions?