Love beyond the Curse

One is BL and the other M/F but both feature a long lived vampire who keeps trying to die until he meets and falls in love with a human. Both dramas have a single, magical way in which a vampire can die.

If you are into a vampire story during Republican era…
Same plot device of fragile young woman who is the redemption of older blase male vampire .

Both MLs are weary immortal beings seeking to die who meet the human FL who is fated to be short lived and holds the key to ending their life. Just when the MLs discover how to die, they end up falling in love.