I was thinking a bit more about how you could portray a weak character. I think that letting her shoot things at all would defeat the purpose. If you have a random, low chance of hitting zombies and ammo is limited, then players will get very frustrated at their lack of input in the game. I think another way should be found to deal with them. If contextual traps are out of the question, then there are other ways for her to combat the zombies that could be more general (eg, implimented in numerous situations) which could make the game distinct from the dime a dozen zombie shooters.

General Gameplay mechanic: She could be trying to get to the stairwell on each level. Each level becomes a puzzle like mission to avoid the zombies.

Whoops: I just redesigned Pac-Man.

Hiding Zones: Dark areas she can hide to evade zombies.

Fire extinguishers could be used to repel/herd zombies, possibly to be finished off all at once in a group with an alcohol and matches combo.

Cublicle walls could be moved to restrict/direct/herd zombies, or allow the player to make safe havens for herself. The more cubicle segments on a level, the easier it would be.

Office pets, tape recorders or radios could be switched on to attract/distract zombies in order to get past them to the exit.

You could make ammo so limited that the player can't even voluntarily fire the gun. She will automatically fire it at point blank range into the skull of any zombies that have latched onto her when she is without armour/on zero health. So, she only uses them when all other options have failed.
Bullets effectively become lives in this senario.

Just a few ideas about how the mindlessness of zombies could be turned against them, the characters frailty preserved, and a unique stealth/zombie herding style of play facilitated.

A thought on the story as well. One of the scariest things about zombies is how quickly a zombie plague can spread, their number swelling exponentially. By having her pass out and wake up with everyone zombified, you could be missing out on some fun story telling by showing the situation go to hell.

It could start out with a few co-workers looking kind of ill, and passing it off as flu or a hard night out on the booze. Later you see two co-workers fighting, with some of the more blokey sorts cheering them on.
A lot of homeless people seem to be wandering the streets outside.
The player's secretary responds to an intercom with a scream, or a groan.
The elevators have stopped working, and the phones are dead.
I'm not sure if these ideas are cliched or not, I've seen a lot of zombie movies at this point!

Eventually it becomes obvious what has happened, as the player witnesses a shambling co-worker advance on a cowering collegue and tear off a ragged strip of flesh with it's teeth, before shambling towards you.

If I knew that the zombie apocolypse was upon me, I know that the first thing I would do would be to baracade myself somewhere with lots of food. Unable to get past the zombie to the stairwell, she retreats to the breakroom, locking the door behind her.
For a few days she lives on what food there is in there, the zombie in the corridor thumping on the door the whole time. Eventually the faucet stops working, and it's a choice between dying in this room, or braving the zombie infested office block.


In response to Fornicolas: Yeah, you're right, what I was suggesting wouldn't really be an FPS any more. Still, even if he doesn't utilise any of these ideas, it was fun thinking about some different ways a zombie game could play out, and how to make it stand out from the croud.
I kinda took the idea of a physically weak female PC and ran with it.

Who would ever think talking about zombies could be so much fun.

These are all good ideas. I do like the falling asleep because when she hits the first floor and tries to exit the building, she could be mauled by a hoard of zombies, tearing her apart and then she wakes up, sitting at her desk. Perhaps she has a copy of a zombie dvd or book sitting on her desk, hinting that it contributed to her dream. That would be a clean way to end it.

Also, imagine drinking coke products controls the zombie disease and it sucks when there's only pepsi machines in the area.