Well the chains don't actually stretch like a rubber band. The pins wear on one side and the holes become oval shaped and thus the chain becomes elongated. It is unlikely that a chain will break but if gets too long, it might jump a tooth or 2 and then the valves meet with the pistons for disasterious results.
This has happened to me. The cam towers are designed to break to prevent damage to the engine but it doesn't always work. I had one camshaft break completely in 2 in the middle of a cam lobe on a 190D. I figured that was the highest stress area when the piston hit the valve.
P E H