I'm pretty sure this class of problem would exist in GC'd environments too unless they're configured to abort on OOM, in which case you'd still be dealing with denial-of-service.

In some environments OOM is a trappable exception, so it's possible that incorrectly authored code would trap the OOM and 'recover' with partially initialized data sitting on the heap. Hopefully it's a memory-safe language so that partially initialized data isn't RCE...