It doesn't. But the company will have to be registered as a U.S. based entity first which may take some time and will only be done after YC starts.

You get a grace period if you leave your job right? I just don't see this as a showstopper...you could've applied and dealt with problems as they came up.

Actually, no. You don't get a single grace day as somebody else has pointed out below. Plus, even if these guys applied and incorporated immediately, they can't (i.e., the INS will not approve it w.h.p.) sponsor H-1s from their own company (even an H-1 transfer) unless the company receives significant investment. All-in-all, it's certainly a big show-stopper.

So how did you guys do it?

We were students on F-1 which turned out to be just the right thing to have. We went on an OPT immediately and by the time we needed H-1Bs for ourselves, we had raised enough money to be able to justify the INS that we are a totally legit company capable of paying H-1B level salaries.

IANAL, but there might be other ways. Send me e-mail. ashu [AT] buxfer

Switching jobs will require a new H1B, normally called 'H1B transfer'.

You can start work on your new job while that is in process, right?

Yes, as long as you filed the H1B transfer application, you can work for the new company. You do not have to wait for the approval or even the receipt (it could be nice to have the receipt as it helps to prove you filed application).