If you really want to mess with their heads, have them hired for a series of runs from Corp 'XYZ' with the requirement that they work with a special operative. Special Operative is of course the Cyber Zombie.
Give your team specific tasks that require their specialized skills, contacts or experience and the Cyberzombie has it's own objectives (perhaps the Corp is conducting field tests with expendable team members .... shhhhh! Don't tell your players!

).
Here is the twist, the Cyberzombie becomes attached to the team (or perhaps a member of the team that shows interest, compassion, comradery etc.) -- perhaps it get lost in the details and begins to think it is human/metahuman again, perhaps a system glitch that identifies them as an asset to protect for the corp at all costs, or just fragging pychosis - it's a cyberzombie!
Next twist - it begins to track, stalk follow them after breaking out of it's facility/fragging it's controller or what have you --- perhaps this would be more fun if you are in an isolated location, like an island where you can't just runaway.

Instead of wanting to kill them, it wants to protect them - this could play out okay for a bit, but is always going to go south eventually. If it is focused on one character it may start disposing of threats (you know, contacts, other runners, that pesky KE officer that's been helping the team out on occasion) so think "Fatal Attraction" with a Cyberzombie. Yikes!
Another spin would be that at some point it begins to feel that the team is controlling it and since it got rid of it's last controllers, begins to take them out one by one --- or the whole team. Don't kill them, but have them disappear until they all wake up at the abandoned soy-meat packing plant. They have to escape and bring an end to the madness once and for all!

Okay, a little melodramatic, but you get the idea - I don't really see cyberzombie focused games as being light-hearted. Although one based on
Cyborg would be a blast!

I just would want have one scene where a player walks into their apartment after a hard day of running, turns on the light and there is the cyberzombie sitting in their favorite chair, silent, unmoving, just - looking at them. MWAHAHAHA! Ahem - I've been reading Girl Genius too much recently; though that would make it a steampunk cyberzombie....hmmmm....off to the drawing board.