If I am playing a game where I have a card in play that makes it so I don't lose from loss of life, and go to -1 life, would I need to gain 2 life in order to be safe without the anti-loss card anymore, or does the negative 'reset' to 0 after damage effects and cards on the stack resolve?
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.