MTG: Is there a lower-limit for life total?
You can go into negative life totals. If that doesn't cause you to lose, subsequent events still affect your life total normally: you could gain life back to zero or above, and losing more life will push you further negative.

The rulings on Beacon of Immortality confirm this:


  2/1/2007  If you double a negative life total, you do the real math.  A life total of -10 becomes -20.  
  
  7/15/2007     Beacon of Immortality's effect counts as life gain (or life loss, if the life total was negative) for effects that trigger on or replace life gain (or life loss).


So yes, if you're at -1 life, you'd need to gain 2 life to get back to 1 life and be safe without whatever was keeping you from losing.