w-2 income with schedule c expenses

My husband works in the construction field as a w2 employee. He has construction deductions that we will claim on a schedule C.
 
My question is this.
 Is it acceptable to have a schedule C with no income? leaving a negative balance?
 or is there a way to make the schedule-C connect with the W-2, such as in the instance, if the Box 13 statutory employee were checked?