The immediate concern for Olivia and the girls was to get Zane to safety, and there was only one place they knew that was safe in this cruel world. They immediately sprinted towards the bunker. Luckily for the party, Eliza had ceased her pursuit out of unfounded fears regarding Zane's potential association with her mother.
Because of this, they were not followed back to their base of operations, nor did they try to evade pursuers. Zane was at 10 HP, which was at critical levels, and had passed out from the sheer amount of damage he had taken.
If he were any other human being, he would have bled to death by now, but for whatever reason, his wounds were not leaking bodily fluids. In fact, the blood sealed the massive holes in Zane's body. A peculiar effect, but one clearly associated with his ability to control his own blood.