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She's probably broody. Different hens are harder to break than others. Two of my hens have gone 1/2 broody, and it was instantly solved by removing their eggs.
I'd try removing the eggs as quickly as possible (and any new ones). Putting her in the run and seeing what she does. If she goes back in the nesting box I'd advise the cage in the run thing already advised...she should eat and drink...most broody hens only go out 1-2 times a day to eat, drink and poo. It may just be that you aren't seeing her doing it. Good luck!
Also, personally for the cage I'd put cardboard on the bottom with bedding... just so her feet don't get sore