Undead PCs

A few years ago I got into a debate with someone somewhere on the interweb--I think it was Rients--about what happens if you roll a 1 for your Hit Points and your Constitution is in the penalty zone: can a character be dead at inception?  Obviously that's not very satisfying, and yet hand-waving a minimum of 1 HP or re-rolling until you achieve a more arithmetically-pleasing result both seem like cop-outs.

Your new character sketch

Then, suddenly, just moments ago, it came to me in a flash: when your Con penalty puts your brand new, freshly rolled PC's hit point total at 0 or less then he/she is undead: you get to begin your adventuring career as a zombie!  The perks:

• You get to re-roll your hit points using 2d8 and ignoring your constitution score.
• No more worrying about things like drinking water, oxygen, and sleep or charm spells.
• Stick with this long enough and you get to be a freakin' Lich.

And some cons:

• Your appetite for brains might be a bit off-putting to your adventuring colleagues. 
• The cleric in your party can use Speak with Dead to force you to reveal embarrassing events from your past.
• Until you reach 9th level -- Vampire -- you might as well forget about getting laid; it absolutely will not happen.