When you die in ZombiU, you will lose any supplies (food, ammo, miscellaneous items, and weapons) you have in your backpack with you at the time of death. In addition, you will permanently lose your player skills that you acquired with that character. Apparently, this is primarily based on the weapons you use. So the longer you survive and fight with certain weapons,then the better those weapons will become. For example, if you shoot a certain amount of zombies with a handgun, then you may earn the skill to get faster reload and draw speed or decrease recoil. Ubisoft hasn't really given any other details but I imagine guns and melee weapons will deal more damage to.
There are also weapon upgrades like more ammo capacity and adding another barrel to a shotgun. Once you get these items, you can go back to your safehouse and sit at your workbench to do a mini game that results in making weapon upgrades like the ones mentioned. The good news is that you will be able to keep your weapon upgrades even when you die.You may lose those weapon, but once you find them again in the environmentthey will remain upgraded.
The player health can withstand a few attacks from zombies, but if you are bitten, then you die instantly.When you respawn as a random new character, you can decide to attempt to backtrack to the place where your previous playable character died in attempt to retrieve your backpack to get the original supplies you lost. When you are at the safe house, you're able to keep a stash of weapons there as well as good and other useful items as back up when your in low on supplies or want to use them for the next chacter you play as since you will eventually die.
You'll also be able to scan objects in the environment as well as zombies to look for any useful items including weapons. The scanner mode will get its own set of upgrades throughout the game. One of the most important things about scanning is to scan zombies to see if they have serum. If they do have some, then you'll use a syringe to extract serum from their body out of a gland. This is what you use to fight off zombies as a last resort by injecting them with it as a counter move. The serum won't be available until later on in the game by the way.

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