Your character is an unliving abomination! A corpse given life, you feed upon the living and live in darkness. You feast on souls and blight the land. That's some major awesome right there and we haven't even got to the bonuses!
Since Space Rock Future is a science fiction setting, you may think it hard to work the living dead into a fairly standard game. The simple fact of the matter is that budget sci-fi is overflowing with excuses to make corpses walk, ghosts fly and vampires stalk the night. Everything from radiation to psychic emanations to mad science to the bending of the time-space continuum have all been credited as potential causes for zombification and if one of your PC's wants to try it, why not let him? After all, they get a bevy of weird abilities that really set them apart.
First of all, Undead are enormously hardy and get twice as many Hit Points as normal. Their bodies are damaged in the same way as the living, but they are almost completely unaffected by it. They also don't have Souls. That was sacrificed or lost a long time ago and now the body is a dead husk driven by either a cruel mind or basic needs and desires. In its place, Undead have Void, which has its own requirements for care and feeding. Void affords an Undead the same Awesome Pool as a living, breathing human, but they do not regain Awesome Points naturally. To get their fill, they must feed.
Whenever the Undead is running low on AP, they must find a living being and incapacitate them somehow. Killing is the method of choice. After that, the Undead must feed on the life-force of the victim, draining one level of Soul for every uninterrupted minute. For every level of Soul stolen like this, the Undead regains one Awesome Point to spend as they please. If they do not kill the victim and do not drain all their Soul, they will recover Soul at the rate of 1 level per week. If they are completely drained of Soul, they will either die from the shock or go mad shortly after. Characters with more than two levels of Soul may sometimes rise from the dead. Rock Stars always rise from the dead. It's in their nature.
However, these "free" Awesome Points come with a heavy price. The Undead body is in a constant state of decay, and one Awesome Point must be spent at the start of every week or the Undead begins to decompose, losing a number of HP equal to its Void every day, until they feed. Most Undead do this without realizing, but Undead with Brains of more than 1 can also voluntarily spend AP to recover 20 Hit Points, at any time, going so far as to regrow lost limbs or repair broken bones.
Due to this talent for regeneration, if you bring an Undead to 0 Hit Points, if it has any Awesome Points remaining, it won't die. It will fall to the ground and be unable to defend itself, but intelligent Undead will be able to spend 1 AP every minute to regain 20 HP. When they are restored to 1 or more Hit Point they are free to rise again to stalk the living. The only way to kill an Undead is to reduce it to 0 HP, then destroy its source of power, normally either the head or the heart. Some particularly old or powerful Undead even go so far as to seal their life-force away somewhere, making themselves effectively invulnerable. A successful hit to this area with a lethal weapon will deal an additional 10d6 damage to the Undead and reduce its Awesome Point total by 1 as it weakens. Once reduced to 0 Hit Points, a strong blow to the source of power will permanently slay the abomination.