According to the Naruto fandom, Rin did ask Kakashi to kill her in order to save Konoha, her village. After a three-tailed beast was put inside her, Rin decided she didn't want the beast to take control over her and destroy her home. However, she wasn't able to take her own life and Kakashi didn't want to, either.

Why did Rin jump in front of Kakashi?

Their purpose was for Rin to return to the village, where they'll undo the seal, kill Rin and have the 3 tails rampage on the Hidden Leaf. Knowing that, Rin jumped in front of Kakashi's Chidori as he charged on a hidden Mist ninja to kill herself and foil their plans.

Did Rin love Kakashi?

It has been confirmed that Rin has feelings for Kakashi. Although it is never confirmed whether Kakashi loved her in return, her feelings would further the already great remorse and anguish Kakashi felt over her death.