The other reply gave good info, but didn't quite answer this. Once an object's core acquires enough temperature/pressure/density to start protium fusion, it will continue, not burn out. The fusion itself increases the temperature, and the produced helium is denser than hydrogen, so the core compresses more under gravity thus increasing the pressure too. So protium fusion creates its own conditions to continue, so there's no such thing as borderline stardom; once protium fusion starts at all, it will continue and it's now a red dwarf. Fusion doesn't begin or occur everywhere, it's still only at the core, but convection will eventually (10^12 year timescale) cause all the hydrogen to have moved through the fusing region.