The Time of the Terminally Ill Extra is a Manga/Manhwa/Manhua in english language, LONG STRIP series, english chapters have been translated and you can read them here. You are reading chapters on www.mgeko.cc fastest updating comic site. The Summary is

As the middle child who is neither the heir nor the cherished youngest twins, Karina has lived her whole life hidden away from others. One day, she found that she only had 1 year left to live. So without a plan, she went to visit her fiancé who she barely knew… To annul the engagement as he always wanted. "I won’t beat around the bush. I want to spend a year here." "....My Lady, have you gone crazy?” "In return, I'll agree to annul the engagement." But she didn't know at that time. "It feels like you’re trying to pretend to be oblivious, so I'll make it clear." "Pardon?" "I like you." I didn't expect to receive his unwarranted interest and affection. I wouldn't have thought I would have wanted to live in my meaningless life.