There are a number of reasons that hens can lay soft shelled eggs. This can happen as they come out of lay as they get older (quite common in the older hybrid bird, as in the industrial market they are never intended to make the grand age of 3), stress (which can include moulting), calcium deficiencies, deficiencies in other vitamins and minerals especially Phosphorus and Vitamin D3, or internal disease such as oviduct problems or systemic illnesses.
If there was just the issue with eggs and she was otherwise normal I would say it is probably just that is coming to the end of her laying life. Sometimes increasing the calcium content of the diet will help with this, as can supplemental D3. Vitamin D3 is usually synthesised in the skin using natural sunlight - not something we have seen a lot of recently!
However the fact that she is now getting soiled, is thin and that you are seeing a mess overnight makes me concerned that she could have a problem with her oviduct and possibly some egg peritonitis. This is a very serious condition that is nearly impossible to treat if left too long. The only treatment really is to remove her reproductive tract - basically to spay her. If there is too much infection in the abdomen then this becomes impossible.
I would get her looked at again to see if there is anything that can be done.
Here are a couple of links I have found that have some additional information on this condition:
The chickenvet site is a very handy site, and they will also advise vets who are unfamilar with chickens if they want any help with a case.
I hope this helps