the old MOT will still be valid, but the driver is aware that the car has defects and is unroadworthy.
if he's still using it on the road, then he will be liable for any accident that the defect causes (skidding on bald tyres for example)
I called the MOT help line on this a while ago.
The police would know before they have puilled him over that his car is not in a roadworthy condition, and he could be fined there and then.
Best tell him to get it fixed.