My neighbor has not water coming out of any of his faucets. (He is draining his tank.) I understand that the sludge in the bottom of the tank could back up and stop up his cartridges or aerators, but how about the tub faucet which has no aerator?

If he has no hot water any where in the house I would start with the water heater. Open the boiler drain to see if there is pressure. Got pressure coming in? Good. The next place I would look is the nipples coming out of the tank. If they are heat trap nipples, (see image) Replace them. If you think that you have pressure in the hot water main then close the angle stops to the nearest faucet and open it up. Now turn the hot water angle stop on for a few seconds. Do you have hot water coming out of the open faucet? Let me know, Tom

Tub faucet has cartridge which has small passages. That's where the debris gets stuck reducing water flow.