This is their cause of death in their past life. Kihoon died and Yeon was just waiting for him and hoping that kihoon return to his embrace—he just waited until he grew old and died. And they met again in their present life because of the red string.
Wasn't there a flashback from Kihoon's perspective where Yeon was badly hurt? That's why in modern times he's scared of Yeon saying he will protect him, because he did in the past and either got badly hurt and died days after or died in his embrace.
Im p sure it was yeon who was hurt in this life, which is why kihoon in the modern life feels an overwhelming need to distance himself from yeon, afraid that if hes too close then something bad will happen to him
This is their cause of death in their past life. Kihoon died and Yeon was just waiting for him and hoping that kihoon return to his embrace—he just waited until he grew old and died. And they met again in their present life because of the red string.