If the universe's expansion rate keeps on getting faster and faster as we observe it today, than eventually all the galaxies will be so far away that we wont be able to see them. The temperature will drop to practically zero degrees Kelvin.
The matter might reach it's escape velocity (exceed the gravitational pull of all the matter in the universe), however space and time will still exist within the vast gaps between the spreading matter. Space-time isn't really a fabric, this is just an analogy for explaining other things. So I can see where you might get the idea that fabric can tear once stretched to a certain limit. However you can stretch space (as long as it exists) as far as you want, there is no limit.
Out side the universe, beyond the 2.7 degree Kelvin microwave radiation, is really the only main place where space-time does not exist.