Can a company subcontract out to a "business" that has no business license legally?

If a "Business License" is really what you mean, the answer is probably No.

Some services, though, do require a license of some sort, like working on air-conditioning systems that have Freon in them.

Another thing to consider is whether some sort of permission is needed to do the job - as in City or State housing or building codes.

What is the work you are considering contracting out?

This individual does auto repair. He painted my car charged $4,000 now threatens to sell the car if I don't have the money is 2 days. He also did engine repair and charged $2,600 that I am not contesting.