Does the Well Stocked improvement apply to epidemic infections?
If the Well Stocked city has 2 supply cubes and is the bottom card of the Infection deck during an Epidemic, you will not remove any cubes.

On page 13 of the rulebook (emphasis mine):


  
  Infect: Draw the bottom card from the  Infection deck. Remove all the Supply cubes  from that city and put them in the stockpile.  (Do not add Plague cubes if the city has no  Supply cubes.)
  


Well Stocked applies any time that city is drawn from the Infection deck, and step 2 of an Epidemic is a draw effect. The exact wording indicates you won't remove any supplies cubes. Users on BGG agree here and here.

Edit: The BGG threads reference the back page of the manual, which makes this explicit (emphasis mine):


  Infection improvements are in effect during:
  
  
  Game set up
  The Infect step during an Epidemic
  The Infect step at the end of every player turn