For me, Firefox 36.0.1 has not crashed but rather FireBug 2.08 starts acting unpredictably with respect to breakpoints.
If I am repeatedly editing JavaScript for a particular web page (web App), particularly if I am adding or removing lines, and have breakpoints set, they can get moved to other lines (and I don't think just a few up or down, based on what I have added or deleted). I can remove the breakpoint from the breakpoints tab, or clicking it on the source line number to remove the breakpoint, but Firebug will continue to stop there. Sometimes a reload of the web page will resolve the issue, but most of the time I have to do more to "reset" Firebug to correct functionality.
It does not seem right to delete all breakpoints manually before I perform a web page reload, to then set them back up for debugging.
Eventually, Firebug will put a throbber where the breakpoint red dot would go next to the page number in the source listing. It won't go away, even after waiting awhile. If I reload the page, the breakpoint is there.
I can't say if this has just recently started happening with this Firefox/FireBug combination because this is the first time I have needed to use Firebug to debug Javascript since late November