If two people sign a lease one moves out without notice who is responsible for there half of rent?

Odds are that the lease holds each party jointly or severally liable for the rent. If that is what your lease says, that means you are 100% responsible for the rent, as is the other person. You are each 100% responsible on the lease. That means you may want to go against the other person, assuming you had some sort of agreement. I may be able to assist you, should you desire. David R. Hartwig 801-486-1715