She said herself she couldn’t run off on her own because she’d have to return to the Covey. I think she was dead before Snow even left the cabin. Maybe slipped and broke her neck or something. She was probably singing while she was still alive and the birds picked up the song.
The Covey probably found and dealt with her remains and they didn’t raise any murder alarm or missing person fuss because she wasn’t shot or anything. It looked like an accident because it was one.
Plus, I think if Coriolanus had even the barest suspicion she was still out there, he’d put every resource toward taking her out. He doesn’t like loose ends. Unless she was able to disappear extremely thoroughly and probably never sing again, he’d have gotten a whiff of her and taken her out. Even if she did run off and survive, if even a rumor of her surfaced, he’d find her.
Even if she did survive, there’s no way she could return to D12. The mayor thinks she had something to do with his daughter’s death, she was known to people there, etc. I don’t think she could have managed to return under a pseudonym successfully.
I also don’t think she’s as resourceful and capable as everyone else does. She’s a performer, more like Peeta than Katniss. She’s charming and clever, but she isn’t a survivalist or a loner and there’s so much that can go wrong in the wilderness. Even a well-prepared, experienced hiker takes a risk going out on long trails. She’s out there in a dress, mucking about in the rain without supplies. I don’t think she’s awful or stupid or anything, but I don’t think she’d be able to hack it on her own.
She’s not even much of a rebel, though she is obviously a free spirit. Sejanus, for me, was the stronger example of the rebel spirit, the need to do the right thing, to take risks for the greater good, etc.
I think she really represents what was left of Snow’s potential to walk the better path. He needed to ‘kill’ her to put away the last vestiges of his ability to connect on a human level, with love. When Katniss chose Peeta, she chose love and life. When Snow turned on Lucy, he turned his back on the same.
It’s one of my favorite books but a very hard read for me because Kate is so much like my mother that it’s eerie.