hey there marko,
I don't know what happens during the blackout itself, I haven't experience one and pray that I don't!
But I guess since those that were able to experience it are able to live to tell about it, it's pretty safe to assume that they did start breathing again after it

.
Also I think I've read somewhere that some freedivers intentionally black themselves out during hard dry statics! Not that it’s something I'm sure they would recommend as a training regimen!
Dive safely!