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, and I imagine this is 100% platform dependent behavior.