Not to be the naysayer here but there is a seeming assumption that she was "surviving" in what we attach to our perceptions as "survival".
The story said she was simply "found living in the woods on the outskirts of the Swiss capital". She was staying in woods near a living area that a community group "owns" so she wasn't out in the middle of nowhere.
Most people don't notice a lot of things in their environments so it shouldn't be a surprise that it took awhile to find her - obviously when she was reported she was found rather quickly.
I personally don't have any doubts that she was moving into the capital area and "surviving" on what she found in that area - maybe even committing petty thefts and vagrancy at times.
It sounds more like she was squatting on the land rather than surviving. I doubt she was pulling down any mad Les Stroud or Bear Grylls skills.
I seriously doubt she was trapping/hunting game, making friction fires, building shelters, batoning wood, or practicing bushcraft skills.
She probably has some form of schizophrenia - the "mission" reference - and was probably in town during the day hours and simply moved to the shelter to sleep. If she doesn't want to have contact with her family and hasn't been ruled or adjudicated mentally incompetent then that is her right but it doesn't give her the authority to trespass.
I've dealt with similar situations with people in my career. Sometimes you even know they're there but it takes time to catch them.
If she was really "surviving" as we think of it I doubt she'd be so close to a town or property.