I have a 97 chevy k1500 350 it wont sta running unless i unhook the vacum hose from the brake booster?

need a little more detail. when you unhook the vacuum line do you plug the end up...so that it won't draw excess vacuum? therefore enriching the fuel/air mixture so that it stays running? if so you either have a bad valve at the booster [ that small plastic adaptor valve that plug,s into the booster],or a bad rubber grommet that it plugs into or a defective /leaking booster unit. if the problem is that it needs extra air [ through the hose] then it's a fuel delivery problem...either carburetor or injection issues. need to know just how your equipped [ carburetor or injection] & just how it's acting at the exact time it stops/stalls...come back & list any details you can...no matter how small they may seem.