If another thread crashes (without relevant signal handler -> the whole application exits), there is not much you can do to guarantee that your application does something - it's up to what the OS does. And there are ALWAYS cases where the system will kill your app without your actual knowledge (e.g. a bug that causes "all" memory being used by your app and the OS "out of memory killer" killing your process).
The only time your destructor is guaranteed to be executed is if the object is constructed and a C++ exception is thrown. All signals and such, make no such guarantees, and contininuing to execute [in the same thread] after for example SIGSEGV or SIGBUS is well into the "undefined" parts of the world - nothing much you can do about that, since the SEGV typically means "you tried to do something to memory that doesn't exist [or that you can't access in the way you tried, e.g. write to code-memory]", and the processor would have aborted the current instruction. Attempting to continue where you were will either lead to the same instruction being executed again, or the instruction being skipped [if you continue at the next instruction - and I'm ignoring the trouble of determining where that is for now]. And of course, there are situations where it's IMPOSSIBLE to continue even if you wanted to - say for example the stack pointer has been corrupted [restored from memory that was overwritten, etc].
In short, don't spend much time trying to come up with something that tries to avoid these sort of scenarios, because it's unlikely to work. Spend your time trying to come up with schemes where you don't need to know if you completed something or not [for example transaction based programming, or "commit-based" programming (not sure if that's the right term, but basically you do some steps, and then "commit" the stuff done so far, and then do some further steps, etc - only stuff that has been "committed" is sure to be complete, uncommitted work is discarded next time around) , where something is either completely done, or completely discarded, depending on if it completed or not].
Separating "sensitive" and "not sensitive" parts of your application into separate processes can be another way to achieve some more safety.