I was reading this manga and the female lead broke up with the male lead because a past love came back into her life and he's sick.

Are there any shows where that happens and she chooses to help take care of him out of obligation or she is guilted into it by the sick guy? She doing this doesn't make her realize how she's hurting the male lead. Eventually the sick guy "frees" her and she tries to win the male lead back. 

Kimi no iru machi?

does being in a mess condition because of his marital problem count? If it is, you may consider to watch All About Eve. 

The FL broke up with the ML to make sure that "her past love" would not do something stupid (drunk or fighting with other people). The SML was actually not really her past love, it was one sided crush.

 Nayeon is Life:

Kimi no iru machi?

Actually no. Kimi was similar, but one thing was different. She was friends with the guy and didn't actually love him.