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Maybe this?
http://www.mangago.zone/read-manga/2345/
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It does seem to be a common theme, ie a gullible character (for various reasons) accepts an illogical story from a stranger at their door. "Youjin", for example. I also remember a couple where people pretended to be the person's cat in order to earn their affection. None were tragedy though, but reading the spoilers in this comment section it seems like this manga is. If you are wanting something more light hearted, try youjin http://www.mangago.zone/read-manga/youjin/
I read a different yaoi manga that has a very similar plot to this one but I can't remember the title. I think it had a happy ending. (not referring to Do S Obake tho, although I love that one)
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