Absolutely possible. If the carrier suspects that your injuries are not as serious as you reported to the doctor, they may assign a private investigator to observe your day-to-day activities. Surveillance can take place anywhere including your home or work. It often takes place at medical visits (doctor's appointments, testing, PT) and immediately before and after. Remember, the carrier knows when and where you are treating, if they have admitted your claim. A PI in an unmarked vehicle will often be waiting in a physician's parking lot prior to an appointment. They will take footage in the parking lot as you enter and exit the building. Sometimes a PI will follow a claimant into a store or office to record. Another place a PI may watch is your attorney's office on the day of your deposition.
Your attorney can obtain video by subpoenaing it from the carrier. Footage can be a powerful piece of evidence for either side. If the defense obtains video of a claimant limping into a doctor's appointment with crutches and then tossing them into the trunk, the claim's value will obviously decrease. On the other hand, if video is taken or reports are made revealing the claimant consistently limped or only uses one arm to preform tasks, the claimant can use these should the defense dispute the validity of their allegations.
It is important to remember the carrier knows a lot about your life once a claim is open, especially when it is accepted. They are paying for your treatment so they know where and when it will happen. They may be sending you weekly checks, if you cannot work, so they know where you live. Your employer is their client, so they know where and when you work. Additionally, their attorney may request to take your deposition so they know when it will happen as well. A carrier can use their knowledge to observe you unnoticed. Therefore, it is important to always aware of your surroundings. Remember, there is no need to worry, if you are always straightforward about the severity of your injuries and how they affect you.