Sorry, I misspoke, was thinking of other DWARF sections. .eh_frame is loadable, but is, of course, like all ELF sections, *mapped* in. In a severe OOM situation, it's very likely that you won't be able to map more pages in, and that not much of it is going to be mapped in at any given time.
(I must have been unlucky with backtrace(). It's never been willing to do more than coredump for me without frame pointers. Mind you I haven't tried it for years because I was so sure it was broken :) time to try it out in my next debugging blitz.)