One of them has Hanahaki disease but because of a misunderstanding the other one thinks its for a love that has been left behind or died.
Hanahaki is a slow killer but every few years the one with the disease dies and the other one has to pull out just enough of the flowers that the one with hanahaki can revive but not enough that all their love is taken from them because he made a promise too his dead love at the beginning.
This is slowly killing the one that does not have hanahaki and the suffering and love he feels eventually turns into hanahaki too which leads to misunderstandings being cleared up and the two getting cured by each other.
Joe/Nicky hanahaki
Hanahaki is a slow killer but every few years the one with the disease dies and the other one has to pull out just enough of the flowers that the one with hanahaki can revive but not enough that all their love is taken from them because he made a promise too his dead love at the beginning.
This is slowly killing the one that does not have hanahaki and the suffering and love he feels eventually turns into hanahaki too which leads to misunderstandings being cleared up and the two getting cured by each other.