My insurance isn't escrowed anymore, but I'm not sure I'm following.
You pay X for the coming year, then pay X/12 into escrow for 12 months. When the mortgage company pays your insurance, you have X sitting in escrow to pay it. If it's not in in there, you're going to go negative or dip into money that's supposed to go toward property taxes.
Whenever I've switched insurance companies and insurance is escrowed, I've been told to send the refund check to my mortgage company.