Lack of maintenance and not doing regular oil changes is the most common causes of timing chains failing and possibly breaking.
The timing chain needs to be properly lubricated as well as the other parts of the engine and if the engine happens to seize then the timing chain can break.
Also if the timing chain loses lubrication then it can start to get hard for it to rotate and then eventually the timing chain can snap.
The gears for the timing chain may also wear out overtime and then cause the timing chain to slip off the gears but it's usually not a problem that happens that often.
Timing chains on a well maintained engine usually last a very long time without needing replaced.
Timing belts however usually last only between 100,000 to 150,000 miles before needing replaced.
But timing chains last a very long time because they are made of steel.