Green card denial, can he stay?

My husband is on an F1 student visa and we just applied for marriage green card & I-765 work permit. He wants to leave his sucky job which is currently sponsoring his F1 once we get the work permit. But we are concerned that if for some reason the green card application was denied, he would need to leave the country immediately since he would have lost the F1 status. Are there any methods of staying in the US for a limited amount of time legally to give us time to apply again in this situation? A grace period or any other applications? Just wanting to think ahead.