That could be a blessing in my opinion. Well honestly if that happens to me I maybe keeping them until the exchange contacted me and ask to return it but since I secured the ETH I would be asking for a compensation for returning it.
Very practical as you secured the fund then it's not that much of asking for little favor if possible. That amount of money will
let you think much deeper before deciding your next step.
Greed inside you will also matter since it's free money where decentralized network is your advantage, no way for anyone to
get it back from you without your permission.