Once the dude is down, he starts making death saves. If someone wants to save him, they can. If he fails three in a row, he's dead. If he rolls a 20, he comes back with a healing surge, and you can try to put him down again.
A warforged doesn't fail his death saves, so you'll just have to dismember him if you want to take him out. Otherwise he'll recover eventually.
Gruunk's Junk In'na Trunk!