Well, sometimes hens lay a shell-less egg, so I wouldn't be concerned about her getting an infection from the yolk. If the shell was soft enough, then it shouldn't have hurt her much. Did it have any semi-hard spots on it or was it basically like a piece of cloth?
She is starting to sound like...
Another abnormality in eggs can be an egg that is too large or misshapen to pass. From what I've heard and read, those are symptoms of a condition known as "egg binding". You might be able to feel the egg if you place your hand back there gently.
Sometimes hens that are new to the laying experience will lay abnormal eggs. Just continue to provide oyster shell, and hopefully it will be gone in a couple weeks. She probably just couldn't pass the soft shell entirely out, so it ended up partially in.