What happens to bitcoins in a multi-sig transaction if nobody signes?
They stay in the block chain, just as normal transactions do.

Let's look at normal transactions first: When someone (A) sends bitcoins to another person (B), B is not involved in the process at all. A just publishes a transaction in the so called block chain stating that only B is allowed to claim the coins. Not before B wants to spend them, he has to prove that he owns them. This happens by putting the signature for the first transaction into the follow-up transaction.

Thus, every transaction stays unsigned in the block chain until the coins are spend in a follow-up transaction. "Owning bitcoins" means having the ability to sign a transaction in which someone sent bitcoins to me.

Multi-Sig transactions aren't that different, you just need more than one signature. As long as you can't provide them the money is frozen, nobody will be able to spend it.