They actually don't have to stop questioning you. Instead, anything they learn is excluded from evidence, and may result in a "fruit of the poisonous tree" problem, i.e. if they learn where you put the gun, they can't rely on ballistics if they acquire and test it. This is a simplistic example though. Fruit of he poisonous tree is a complicated doctrine, and there are exceptions like inevitable discovery. Nonetheless, it's usually a good idea to stop the interrogation.