According to Jori's comment.
Hashi +1 buff still displays even if he dies.
Scroll down...
Ref : HERE
Hashirama's passive when skill broken does become a non-removable as it becomes a permanent buff as long as the ninja that casts it is alive.
However, the passive does disappear when the ninja dies.
This is the same for other non-removable passives such as the Madara/Konan example given by ICE*:

Sorry for any confusion and I hope this helps clears it up.
~Jib
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