The inner workings of motors and generators
It gets its power from the built up magnetic field. At this point what
  happens to the magnetic field?


What is "held" in the magnetic field is energy not power and, when that energy reduces to zero, the current also arrives at zero. 

When the current becomes zero there may be a little bit of magnetic field that remains and this depends on the inductor core material and how much the original driving current saturated the core. 

What remains of the magnetic field cannot be converted to energy and represents a loss of energy.