What would you do if you had a soldier with a permanent profile (for running) and you saw this soldier running for exercise?

Nothing. Obviously the soldier is trying to get a good workout in. Usually profiles are run at own pace and distance. Unless the profile specifically states no running, leave the soldier alone. Also, as someone who ran with a P2 profile, some days you feel better than others. I may run today with no problem and next week my whole left leg could swell up for simply kicking a few lieutenants in the chest.

First of all break out the camera, video tape if possible or get witnesses. Next make sure profile eliminates ALL running and not states "running at your own pace". Next counseling statement and inform your PS of the situation.
Seems to me if the soldier needs exercise, then I bet you can find some work that will help exercise this soldier and burn up some energy.

Take it case by case. I tore my rotator cuff at an army school and was already seeing chiropractor for back injuries once a week. Forced to have a profile. Normally I'm am a 300 pt score type guy, lead from the front !! My profile was basically a dead man profile. But, once I felt strong enough I started to work my self back up to par, (286 on APFT first test after profile lifted.) If I had someone report me without talking to me I'd be pissed! If an NCO can't speak to the SM AND HANDLE AT THE LOWEST LEVEL... Take off your stripes. If the SM is I dirt bag and shaming handle accordingly. But, either way do your due diligence and ask yourself what you did to help, guide, or mentor before you throw them under the bus. Golden rule still applies, how would you want to be treated if it were you in their shoes. Trust me, I'm a hard ass... 210 is the apft standard for my joes, 220 for NCOs 270 for myself, but pissed if not a 290-300.