Several years ago a popular gaming forum with a significant teenage audience I used to read had declared a simple policy toward threats of suicide. If you were threatening to kill yourself, do it, and stop messaging the mods, they are not here to talk you down from a ledge. It seemed pretty effective.
Most these threats weren’t serious, just some problematic teen looking for attention. Showing them that some strangers don’t give a shit about them or their antics could be a real eye opener.