When a process crashes I want the possibility to invoke gdb (or a similar debugger) against it in that crashed-but-not-cleaned-up state. Often post-morteming a core dump gives enough information but sometimes I want to explore the running state further, possibly suppressing the immediate fault and running a little further. It isn't always appropriate to run the process under gdb from the outset (e.g. where the invocation is complex or the bug is absurdly timing-sensitive)
What I'm describing is basically the just-in-time debugging facility that is exposed on MS Windows through the "AEDebug" registry key: leaving the faulting thread suspended while doing something diagnostic. On non-developer Windows PCs this is commonly set to a crash diagnostic mechanism (formerly "Dr Watson"), for which the Ubuntu equivalent seems to be "apport".
I did find an old mail thread (2007) which refers to this question "popping up every now and then", so possibly it exists but described in a way that eludes my searches?