If your previous H1 has expired than you will be accumulating out of status days.
If your previous h1 has not expired , INS might take a liberal view based on the circumstances. Remember, you need recent 2 paystubs to transfer h1. So your latest paystub will serve the start of out of status/job . If you are out of status for more than 6 months, then you might invite 3/10 year bar from entering US.