The problem is that Jane can no longer spend the coins. So what can she do with them?
In the hypothetical, Jane does not handle GEC: Stewart does so
in her stead (and without her knowledge) through an input-less transaction (to account, in GEC, for her fiat transaction with John, a GEC holder).
I have no idea what you describing then. Try again to explain what is going on and this time please use the English language clearly.
Why does Jane give fiat to John if she gets nothing in return? How does Stewart get fiat? Does John give it to him?