This is not the Inspector XE related issue, I mean you can run application with/without Inspector XE when meet an unhandled exception, core file will be dumped - if you enabled "core dump". Please see:
Here I have to mention other thing - Inspector XE can break to an error in code and continue debugging with gdb.
[root@kentsfield-01 problem_report]# inspxe-cl -collect mi3 -knob appdebug=on-error -- ./test_memory.gcc
Used suppression file(s): 
Stopped at uninitialized read
- waiting for debugger to connect...