If you received no benefit from the work this subcontractor performed, then you may be legally justified in not paying him/her. However, that does not mean you won't have to defend a lawsuit. Even worse, the subcontractor could claim that he/she is really an employee entitled to wages for that week no matter what, and then you could be liable for payroll taxes and the employer's share of social security and other withholdings such as unemployment. If this subcontractor files a claim with the Department of Labor, it could open a whole can of worms regarding whether your other subcontractors are employees or independent contractors. On the other hand, if you pay this subcontractor for the week, your other subcontractors who have not been paid under similar circumstances also could complain to the Department of Labor (although you would have a stronger, but not bulletproof, defense against them, since you have signed agreements).
The information provided above is for general purposes only. It does not constitute legal advice or create an attorney-client relationship. Seek competent legal representation, because the facts of each case are different.
If you have a prior relationship with this sub-contractor, and a pattern and practice whereby you previously entered into such signed agreements with the sub-contractor, or it was well known in your industry that you (or others in the industry) required such agreements with all sub-contractors, then you may be able to argue that you entered into the same agreement with the sub-contractor this time. You would then contend that the fact that the agreement was verbal rather than written is not dispositive. Otherwise, you may have a difficult time avoiding paying this sub-contractor.
This is a general answer and no attorney-client relationship has been created by these communications.
While you could argue that you do not have to pay, I think it is the weaker argument, and you should look to settle this claim before litigating.