Rule Question : When life becomes untenable...?

2nd ed of apocalypse world says that when the PC's harm countdown hits 12:00, the players have the 4 options to choose.
and then all of the playbook contain harm countdown and "when life becomes untenable" option list.

Playbooks, seem like once PC chose one of those option, next time her life becomes untenable again, she couldn't choose that option because she already you checked it off. however, I couldn't find any kind of statement on rulebook.
Is it stackable? PC can choose the option she already choose? of course not dying twice. come back with +1weird twice or come back with -1hard three times. I hope they couldn't

One more thing, if you should check the options off, when changing to a new playbook-untenable,improvement whatever-, Do "everything belonging to her" include checked "when life becomes untenable" option list?

Right. Things that are checked off or filled in cannot be used again: that's why checkboxes are used. It is the same for advancement options.

As for whether those things belong to the character, when changing playbooks, that's going to be up to the MC and the player to figure out, same as everything else. Sometimes it might make sense that those options are refreshed, sometimes it might not. I think in most cases, that sort of near-death experience is likely to carry over, but I can certainly imagine a situation where the new playbook represents a deeper sort of rebirth or rejuvenation, and maybe then those past hardships are forgotten.

In my experience, when a character changes playbook, especially after a death: they're really not the same person they were. The things they cared about (that which came form the prior playbook) were no longer important to them, and so in every play case we've discarded the features and possessions of the prior class. Although, the story reflected this change in a very real way as well, so there wasn't much argument / bartering to be had over them.

Either way, we left all of the untenable checkboxes filled.