Common Lisp (SBCL), 79 bytes.

SBCL captures pretty much every exception and signal, but we can cause an "Unhandled memory exception" which is the result of a SIGSEGV. We must tell SBCL to not consider type safety and just add a fixnum to a float, which ends up disastrous.

(defun f(x)(declare (optimize (safety 0))(fixnum x))(the fixnum (1+ x)))(f 0.0)

My SBCL image errors with:

Unhandled memory fault at #x14.
   [Condition of type SB-SYS:MEMORY-FAULT-ERROR]

Evaluating (f '(1 5)) returned a garbage object, then (gc) threw Lisp into the low-level debugger after it tried to GC that object presumably. I don't see the difference in results since it is possible to jump back into Lisp from this state.