Mona Grant is a former singer and the wife of Eddie Mars. There are rumors that she ran away with Rusty Regan, but you know what they say—never trust a rumor. When Marlowe is finally able to track down Mona's hideout, we find out that that she had agreed to go into hiding to protect Eddie so that the police would continue to think she had run off with Regan.
So what exactly does this say about Mona's character? Well, our sixth sense is telling us that Mona is crazy in love with her husband. She's willing to give up her entire social life and go into hiding, just to keep Eddie out of trouble. She even shaves off all her hair to prove to Eddie that she'll do whatever he wants. Now that's love.
Mona's loyalty to Eddie is what attracts Marlowe to her, and she even helps Marlowe to escape. Mona represents the only female character in the novel who is pure and honest, so it's not surprising that he develops quite a crush on her. But in the cynical world of The Big Sleep, the boy doesn't get the girl because the only love-worthy woman is already taken, so Marlowe is forced to remain a lonely bachelor.