Break when exception is thrown

Go to the breakpoints window, there's a button that looks like J!, there you can set breakpoints for Java exceptions, either caught or uncaught. You can reference classes or use pattern matchers for exception names.

Also, under Window -> Preferences, Select Java -> Debug and there's a checkbox to tell the debugger to break on uncaught exceptions

You are able to define the precise list of Exception you want to have a breakpoint on, even if those exceptions are uncaught (which should be the equivalent of "unhandled")