Question about Wolverine in X-Men Munchkin

[Jato]

Hello, I have a question about a game interaction that happened yesterday during a match of X-Men Munchkin.

My friend had the "Wolverine" ally at the start of his turn, which states you cannot lose him to traps or bad stuff. During combat, he suffered the bad stuff from Lady Deathstrike, which kills the player.

In my interpretation, if the player were to die, he would lose all his allies, but he argued that Wolverine would be protected from this interaction since the death was caused by "bad stuff."

Can anyone clarify what is the correct interaction? Would Wolverine survive Lady Deathstrike or would be be discarded from the player being dead to the effect of Deathstrike's bad stuff?

Thanks,
Jato