This drama story sounds a lot similar to an anime I saw once Named Orange.

In Orange, the main character’s past self sends letters to her future self giving notes on how to prevent her lover’s death, so not really…since there are quite a few plots with a storyline like this.

There is this Manhwa called Seasons of Blossoms and it depicts the life of  group of friends and one of the stories from there reminds me of this...it's the Lee Hamin's part. The story is quite similar as the plot is centered around the ML, who later suicides and the FL...the thing is there is no time travelling but here also the FL has not moved on in her life from that incident or recovered...the synopsis just reminds me of it a little bit

 xiaotii :

I'm reading Seasons OF Blossoms but I'm pretty sure it's Lee Haemin's brother who commited suicide not Lee Haemin himself. The girl who was his brother's girlfriend is the one who's unable to move on, not the female lead because she's in love with Bomi who's the male lead not Lee Haemin.

 looks like you got the names confused Lee Jaemin is the name of the guy who is friends with Bomi and Lee Hamin is the name of the brother of Lee Jaemin who suicided .... I considered the brother as the ML and the girl who  lost him as the FL because the story centered around them in a way when Bomi gets together with Jin Young well but it still doesn't change the fact that Bomi and Jin Young are the leads ^^

I don’t remember the name of this manga but it’s about a girl who travelled back in time with the help of a mysterious being in order to meet and try to save her boyfriend from death. I think this show might have taken ideas from several different plots.

There’s also an anime movie named “The Girl Who Leapt Through Time’ but the only similarity is the manipulation of time plot so.

There's also a webtoon called Back to You that I personally instantly thought of.