With the first ability, you don’t lose the game if you have a life total of zero or below. In most cases this is great and keeps you from losing, however Phyrexian Unlife’s second ability changes how damage is dealt to you. Instead of damage affecting your life total, Phyrexian Unlife makes it so all sources that would damage you are treated as though they have infect. (It does not actually give any object infect, the game just treats it as it does when it deals damage to you.) This means that instead of your life total going down, your poison counter ‘collection’ will go up.
There are a few things to keep in mind about how this card works. The first is that you cannot pay life that you do not have. If your life total is below zero, then you can’t pay life at all. Another thing to point out is that you can lose the game with a life total of zero or below once Phyrexian Unlife leaves play. So in some games a well times Naturalize can be a kill spell.
Finally, if you control both Phryexian Unlife and Melira, Sylvok Outcast you cannot lose the game due to damage. The Pyrexian Unlife makes it so all sources that would damage you would give you poison counters and Melira prevents you from receiving poison counters.