Protected batteries will shut off at a prescribed voltage and employ over-current protection. My 14500s don't even get noticeably warm during charging, but I don't charge them unless I am nearby to monitor things. Protection circuits can fail, short, and cause meltdown, so nothing is perfectly safe. Even IMR batteries using safe chemistry have been known to spew and explode when they failed and the vents couldn't exhaust the pressure as fast as it built up.
Watch them, don't leave them charging when you aren't around to check them, don't mishandle them, drop them (damage), or let the spring loaded contact in the charger hit them hard when you put them in the charger. The protection circuit is in the flat end where the movable, spring loaded contact touches the battery. Sharp shocks can damage it.
I tend to think that battery failures are largely aided by handling and lack of care and improper applications that lead to excessive drain loads. Back when there were news reports of laptop fires caused by Li-ion batteries, the failure rate was way less than 1% and that was traced to a manufacturing process error.
