Universe becoming finite If sometime in the distant future, the Universe stopped expanding, would this mean that the Universe was no longer infinite?
If the density of the universe is high enough then the mass of the universe would be enough to eventually stop expansion and cause the universe to contract (the critical density is about $10^{-26}\, \mathrm{kg\, m^{-3}}$).

If this is the case (it's probably not, the universe is probably flat, with dark energy causing expansion to speed up) then the universe is finite in time and always has been. The universe doesn't stop being "infinite".