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I understand the question so that the story continues after the (postponed) death. Usually the reader knows how far into the story he is, so if there's too much story left, the reader will know, or...
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Source: https://writers.stackexchange.com/a/12646 License name: CC BY-SA 3.0 License URL: https://creativecommons.org/licenses/by-sa/3.0/
#3: Attribution notice added
Source: https://writers.stackexchange.com/a/12646 License name: CC BY-SA 3.0 License URL: https://creativecommons.org/licenses/by-sa/3.0/
#2: Initial revision
I understand the question so that the story continues after the (postponed) death. Usually the reader knows how far into the story he is, so if there's too much story left, the reader _will_ know, or at least expect, in advance that the first-person narrator will not die (unless it's a ghost story, as Jasper guessed). But then, tension may still build up on what event will cause the suicide not to occur, or to occur but not be successful. After all, in the classic criminal story we know from the beginning that the crime will be resolved. Yet it would be a bad criminal story that would not build up tension anyway, because we don't know in advance _how_ it will be resolved. The more you make the suicide seem inevitable, the more tension there will be how this suicide is ultimately avoided. Of course if that postponed suicide is close enough to the end of the story that the reader could reasonably expect it to occur at its end (or you're not close to the end, but the pace of your narration makes it still reasonable to expect the suicide to be at the end), then the question of whether the character commits suicide may of course also be a source of tension. Note I've not read your short story, so I can't comment on if it creates tension as is (but then, given your spoiler I would have known what will happen anyway, which certainly reduces the probability of tension building up significantly).