Lol that is really funny, i actually don't know, i think it will be like in the movies, the zombies will be brain dead looking for the living to eat their brains and then then those who brains got eating will became zombies and go on like that for some time, so lets say that a living has a wallet and then gets bitten and became a zombie, so is not in control of his coins anymore, only if he saved the private keys  on paper somewhere and put it on his pocket and then is a zombie and then go to eat brain of someone and then this guy bash him with a baseball bat and once is double killed he looks inside his pockets and find the private keys then he can use it and import into his wallet, now the interesting thing is that when this happens there will be some kind of a burn and a deflationary equation will make the market cap of this coin to increase and probably overtake BTC because as we know with BTC they want to implement the lightening network and this will never works on a zombie apocalypse scenario, so the only thing that is pending is launch some satellites into the space and do a testnet similar of what TRON did when swapped from the ERC20 token to his own blockchain, so it can be possible to do something similar, create a token on ethereum and then do the swap immediately after the first zombies show up, it will be hard but i think almost everyine will be dumping all coins to buy ZombieApocalipseCoin.
Zombies are brain dead so there is no need to worry about them, if they hold some coins there will be practically burned.