If this happens to you, you may ask yourself, "What are they looking for?" The insurance company is spying on you because they are looking for you to mess up. They are looking for any contradiction between what you claim your physical abilities are and what you are actually capable of doing when you're at home. So, if you have workers' comp for a back injury, but the insurance company snaps a picture of you moving a heavy box, this could ruin your claim. It's a lot more common for insurance companies to spy on people with large amounts of workers' comp than people with PI claims, but you never know.
If you see a suspicious car outside your house and think it might be an investigator for the insurance company, check it out. There is no law stopping you from introducing yourself. Ask your neighbors and see if they've noticed anything different. But as always, follow your doctor's advice and don't do anything that contradicts with what you've claimed your physical limitations to be. Claimants must be honest if they hope to receive any compensation or medical treatments for their injuries. Even if you are being watched by the insurance company, as long as you aren't doing anything outside of your medical restrictions you will be fine.
Other articles you might be interested in:
What Can I Do If I Know I'm Being Watched By the Insurance Company?
Why Future Medical Treatment Can Affect the Value of Your Texas Accident Case
You Must Report All Your Injuries to Your Doctor
Insurance Companies Are Your Friend, Until They're Not
Do You Need An Attorney?