Volume 1 of Pieta (reviewed here) left us with a pretty grim scenario.
Thankfully, the jump does not kill Rio. It turns out that she will be able to recover fully, but Sahoko and Rio's psychologist Minori-sensei know that she'll try to commit suicide again unless what caused her to do it is actually dealt with.
They figure out that it was Rio's stepmother's doing. She owns up to her culpability and makes it clear that she'll do whatever it takes to remove Rio from the Martha Stewart fantasy of a life she wants by committing Rio to a mental institution as soon as possible. Even Rio's father is disturbed by her, and he tells Minori-sensei the truth about what his wife told Rio. Minori-sensei clears things up for Rio, and she decides to divorce her family. In one of my favorite scenes, Minori-sensei tells Rio that he and his wife have wanted to adopt her as a daughter for a long time. Even if she doesn't want to be adopted, they're still there for her if she needs anything.
As Sahoko continues visiting her in the hospital, Rio gets over her fear that she'll hurt whoever she loves. We also learn more about what caused Sahoko to become a hikikomori for a full school year. While Rio has a truckload of horrible family reasons for her issues, Sahoko comes from a perfectly functional, loving family. The explanation for her withdrawal from society works because, well, you don't need to have a traumatic childhood to have problems interacting with people. Some people are just like that. While Rio wore her problems on her sleeve and acted out when we first met her, Sahoko was that girl who hides her problems desperately in order to create normalcy in some sphere of her life. After she gets over that by opening up to Rio, she's able to actually feel relaxed and happy instead of just pretending to be. In short, both of their behavior from the beginning of this series makes sense.
Let me go on a small tangent. When Pieta was published, it was still popular to link mental illness to lesbianism in manga. Pieta subverts that by making its characters' issues have absolutely nothing to do with their sexual orientations or who they like, instead making Rio and Sahoko's love what helps them overcome their problems. You'll find thematic similarities in the recently popular Blue Friend by Eban Fumi, which seems pretty clearly influenced by Pieta, if you're looking for something similar in yuri. I also recommend Fuyumi Soryo's Mars, a non-yuri shoujo title that feels similar as well.
Rio's stepmother tosses out Rio's things and moves her own things into the house Rio occupied, but in a delicious bit of irony, the house catches on fire. Rio's possessions stay safe and out of the dumpster because of Sahoko picking them up and storing them at her house.
After leaving the hospital, Rio moves in with Sahoko. This series addresses the issues that could, realistically, come with Sahoko already deciding that she wants to spend her life with Rio by having Minori-sensei and his wife discuss them- satisfactorily, I might add.
Rio and Sahoko help each other study for their entrance exams and start college, looking forward to their lives together
We get a bonus chapter showing them spending a week at Sahoko's aunt's beach house, where they send an omiyage to Minori-sensei and his wife.
A sweet conclusion to a roller-coaster ride of a series.