While the idea of wearing a vest that contains a series of electric wires might seem a bit risky, these products are entirely safe for use. Not only do the wires carry a very low voltage, but there are multiple protection systems in place to make sure that nothing goes wrong. If the wires short out or get disconnected in any way, the power supply simply cuts out.
The second system is a heat sensor which will turn everything off if the battery is getting too hot. The truth of the matter is that the battery is more dangerous than the wires, but systems like these are guaranteed to prevent any serious malfunction.