Phyrexian Unlife won’t affect damage that reduces your life total from a positive number to 0 or less. For example, if you’re at 3 life and are dealt 5 damage, you’ll end up at -2 life. The next time you’re dealt damage, it will be dealt as though its source had infect.

If you’re at 0 or less life, you can’t pay any amount of life except 0.

You can still lose the game for other reasons, including having ten or more poison counters or drawing a card from a library with no cards in it.

If you’re at 0 or less life and Phyrexian Unlife leaves the battlefield, you’ll lose the game (unless some other effect is keeping you from losing).