I have a girl that does the same thing. She will occasionally lay just the insides of the egg. No evidence of a shell at all. She's about 1 1/2 yrs. old - a black sex link - and has never been the best layer. She has twice stopped laying for a while and then had a rough time getting her system back in order to start laying again. One time was right after molting. She'll do the egg with no shell at all - usually on the roost like you're talking about - then a soft shell - and finally back to normal eggs.
There was one time that I thought she had something serious going on. She hadn't laid for a few days and then acted like she was egg bound - lethargic, puffed up, etc. She then laid two in one day [yes, it was her as I saw her drop one in the run and then watched her get off the nest with the other] - both with soft shells - and finally got herself back into rhythm.
The last time my girl did this was this past spring. I changed food on them - went from fermented feed to layer pellets only and she almost immediately began having problems. Put her back on fermented feed and she went right back to laying decent eggs. I don't know if the change in food was the problem or just a coincidence. I think this girl of mine has some sort of internal issue and that she'll always be like this. Fingers crossed as she's been laying consistently hard shelled eggs the past few months.
Has your girl molted or had any changes that would impact her? Been frightened by anything? Hope she gets herself turned around!