Felon said:

OK, not real clear on the response here.
An arcanist is down 10 hit points. He cast false life and rolls 10 hit points. He's not healed, he just has a pool of 10 hit points he's sitting on. But what if he's at negative hit points when he casts false life? He's not positive then?
And what if those 10 temp points get used up? He can't cast false life to replenish them?
First, if mage is at 10 hp, casts false life to get 10 hp, and gets hurt for 8 hp (leaving 10 real hp and 2 temporary hp), he can cast false life again. If the result is more than 2 temp hp, the stronger of the two false lifes on him will "count" and he will use the 2nd casting of false life (say for 11 hp) instead of the "old" one of 2 hp. Thus it can make sense to cast false life twice, if one has lost some of the temporary hit points after having cast it the first time.
Second, if a mage is at negative hit points, he is usually unconscious. If you mean the mage would be at negative hit points, but the current false life temporary hit points gives him a positive total, then the mage is fine. To see if he is conscious or not, add his regular current hit points to his temporary hit points, and subract any nonlethal damage. If it is a positive number, he is fine. If is a negative number, he is not fine. If it is exactly 0, he is kinda fine, kinda not.
Third, if the temporary hit points get used up, the mage can cast false life again to get more temporary hit points. However, "Real" hit points don't get healed by false life. Thus a mage living on "false life" hit points is in trouble (much like slow poison), as the spell has a duration that will run out. But it gives the mage time to find a cleric or healing potion.
But it is actually quite difficult to get into the situation of having negative "Real" hp and positive temporary hp, as the temporary hp are always the first to go when one gets hurt. That is sort of the point.
Hope that makes some sort of sense.
edit: If anything I say contradict what hypersmurf says, go with hypersmurf.