Black holes

Assuming that black holes never "stop", what would happen in the future when a black hole becomes so large that it pulls in the entire universe?

Black holes do not grow in size. The accretion disk does.  Anything outside the boundries of the black holes gravitational field wont be effected.  Hence why we have not been pulled into the supermassive blackhole in the center of our galaxy (because 5 billion years is enough time to do that). Not to mention the popular theory is that like mini-black holes, black holes in general "evaporate".

Look it up.