Can Standard legally follow someone and look through their personal stuff online?

I am writing this on behalf of my wife because she had just gotten a phone call from the Standard Insurance Company. They are trying to take benefits away just on her mental status of being diagnosed with severe depression by her internal medicine doctor. The benefits she receives were based on her severe migraines diagnosed by her neurologist. Both doctors have written letter stating that she is disabled from working indefinitely and cannot hold down a job. Several weeks ago she noticed someone following her just simply dropping off and picking up our son from school. And a 3rd time just going to get groceries and her medicine for her migraines and fibromyalgia. This is a rare time for her to get out when she felt good maybe once every 6-9 months. Her being followed it scared the mess out of her then called 911 after that they stopped. This was admitted in this phone call that they had someone follow her and they also admitted getting personal stuff of hers on the Internet even a Facebook she started while still working almost 3 years ago. Just to get extra money on her own from home. She hasn’t used that page in 2 years since the doctors told her no more work. The Standard told her that page could affect their decision. She told them everything was true and she asked them why are they trying to take the benefits away on her depression when they given to her based on her severe migraines. They would not answer her about that. She even told them if they took benefits away we could lose our car, power cut off and any other utilities because I bring home only $800 a month. Of course they showed no sympathy. I ask one can Ltd insurance companies legally follow someone personally and look at personal stuff online, and what suggestions are there to keep her benefits without taking the standard to court if she gets denied and loses her appeal through them.