No, this is not possible. To begin with Face ID is a face recognition system. It does not take a picture every time someone tries to access your phone. If they were unsuccessful, it did what it was supposed to do because it didn't recognize their face, but it didn't take a photo of their face to begin with.
Don't leave your phone unattended where someone could try to access your phone. Once the phone couldn't recognize their face as you, they would have been given the opportunity to try to enter your passcode, which you should NEVER EVER share with anyone. Had they tried enough times to enter a passcode which was not correct, your phone could become disabled, requiring you to erase it to get back in.