Timing belts most of the times function well and then suddenly they tear break causing massive damage to valves and pistons, because everything loses synchronisation and pistons hit valves when they are open. Some engines are engineered in such way that this is not possible (eg. GM\Opel\Vauxhall\Holden C20NE).
But such failures that the belt doesn't break completly, but rather stretch are also found. it causes marginal timing change, but i guess if it was en extreme case it could affect vehicle performance.
Timing belt can also get damaged if one pulley or another breaks and belt can touch some static surface (eg waterpump or engine block). It becomes thinner and thinner and in the end will break prematurely.
such things happen, but a tech with 3 month of experience probably won't know that and will only rely on what diagnostic interface says.