They're just less likely to wiggle out (most chains break because a pin has moved, not because a plate snaps). On a derailleur bike a broken chain is a minor problem because you can fix it with your trusty multi-tool. On a fixie it's a bit of a disaster, because, even if you have a tool, there will never be enough chain to reach around (huhuhuh...he said "reacharound") both sprockets unless you find all the pieces.
I carry a couple of spare links on long rides.