Q:

very fine solenoid wires won't burn from AC source?

I've seen tiny solenoid electromagnet (that is the solenoid used to open contacts inside a GFCI receptacle) with very fine wire used in the winding.. won't it burn if exposed directly to 120v ac power at each end? 
How is the winding computed? 

A:

Wire thickness doesn't relate to voltage.  It relates to current.  So a coil of that nature would either need to be externally current-limited (resistor in series), or internally limited due to its own practical impedance, being a coil and all.  In that impedance, frequency would be a factor. 
Insulation thickness relates to voltage. And coil wires don't need enamel strong enough to block the entire voltage, only the worst-case voltage between adjacent windings.  If each winding layer has a separator with higher dielectric strength, that may be all that is needed. 

