Since it can't fall off, that enzyme molecule is dead. If there's too much product, the enzyme which makes it is inhibited and the rate of production slows down. Another control mechanism is called allosteric control. This resembles non-competitive inhibition in that there are two sites, an active site and a control site. Molecules called regulators can bind to the control site and change the structure of the enzyme.
Some regulators actually improve the geometry of the active site and make the enzyme more effective.
Such regulators are called positive regulators. Other regulators reduce the effectiveness of the enzyme and are called negative regulators and are thus like non-competitive inhibitors. All the known enzymes which work this way are made up of at least two protein chains. Since allosteric control can both increase and decrease an enzyme's catalytic efficiency, it provides very fine tuning of enzyme activity. The body also can regulate enzyme activity by changing the enzyme's concentration.