You can fix a sink that won't turn off by replacing the faucet. When you shut off the water under the sink, the faucet should stop dripping. If it's dripping, then the faucet is leaking. To stop the leak, you'll need to replace the faucet.Go to the basement and locate the shut-off valve for the water under the sink. Turn it clockwise all the way until it won't turn any further. Open the faucet and see if water is still running into the bowl. If water is still running, it is likely that the knob is stripped or the metal pipe is bent.This is an easy problem to solve. The first step is to turn the water off to the sink at the wall. The second step is to locate the ball at the base of the faucet. It’s located beneath the faucet handle and is attached to the stem.