There's a lot of death-as-a-consequence-for-losing here, but what about events where you have to die to qualify such that the winner can never know if they won. The ones suggested by >>18753 under New sports are really good. I was also already thinking of their implementation of diving.

My examples:
> Synchronised drowning.

Two teammates must both drown themselves in a bath-like chamber where a transparent cover keeps their lower body in, and they have somewhere to clip in a bar above their upper body to help keep themselves under. If both of them successfully drown themselves, they are judged on how in sync and artistic their drowning was, otherwise they are disqualified. Giving in to survival instinct could really let your teammate down.

> Synchronised roasting

Similar to above, but their both locked in separate ovens instead of having to keep themselves underwater. There is no longer the possibility of disqualification due to voluntary survival, as they are locked in.

> Pole Vault/High Jump

But there's a death pit after the bar that contestants must land in, and they are disqualified if they ever learn the height an opponent of their's set their bar before they die.