The ITCs will give you a credit refund to your account with Revenue Canada. Not a NIL remittance. They will send you a cheque, or deposit direct to your business account if you've set that up with them.
I've had ITCs that exceeded my GST collected on sales in a quarter, and received a refund of the difference. Once it was after a large purchase in a quarter, and another was after little or no sales but with ongoing expenses related to business.