When ECs are converted the keep their SA as long as it's something 'a hero would do' i think. Not positive, though. It's a kind've sketchy ruling sometimes.
That hasn't been the case in years. But that's what most people seem to remember.
The REG says the following:
"If a Hero is converted to an Evil Character, it’s special ability does not work. If that Evil Character is later converted back to a Hero, it’s special ability works again."
"If an Evil Character is converted to a Hero, it’s special ability works as long as it does not harm Heroes."
(A note I've added several times: that's kind of meaningless, because harm is defined as "any effect from cards not of the same alignment (i.e., good, evil, or neutral) targeting a character.")