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Fitbit monitors a persons "VITALS" via electronic (voltage) signals. We are the Body Electric!
A stun gun introduces a higher (and much 'noisier') voltage than than what our bodies normally create within.
Fitbit is designed to detect normal, body-level voltages. Voltages many times greater than what the Fitbit expects would cause the device to read off the chart and possibly be destroyed (depending on how close the stun gun electrodes contact point is to the attached Fitbit).
Also note that Fitbit monitoring is not medical grade monitoring. There are a few factors involved, such as contact integrity and stability: is the Fitbit making good, conductive, non-moving contact to the person's skin or is contact loose and moving? This affects not only signal levels but signal 'shape' and level variance. This discussion could become more complicated, but it isn't necessary at this point.
All we need to know is if a stun gun is close enough (contacts the same limb on which the Fitbit makes electrical sensing contact, within guessing 15-20 inches) to the Fitbit it will affect its detection and the data would indicate data not possible for a human body to generate on its own.
If the stun gun makes contact on a different limb, such as a leg or maybe on the neck the Fitbit likely would detect normally and record the person's physial reactions to the stun gun jolt: increased/spiked heart rate and a change in altitude (fall down) if the Fitbit has that capability (feature to count ascending/descending steps/elevation).