I have a really hard time understanding how gravity waves would survive the Big Crunches. Probably my failure to understand comes from how I think of space.

If all matter is re-crunched into a "singularity," then no space remains? Right? Or time either?

Where do these residual gravity waves exist? If the void of nothingness? That seems wrong.

I guess based on the article that the theory proposes that not everything is re-crunched (dubious?) but that some stuff remains in the universe (dead black holes are somehow not re-crunched?), and therefore space and time do not cease to exist between Bangs and Crunches?

I don't know. I just don't really understand, which is fine as I am a brain scientist not a physicist.