Technically speaking nothing stops you from cancelling the card and booking a room at a lower price, especially if you're planning to travel to a different country. Theoretically speaking the hotel can attempt to sue you for non-payment of debt, but this is quite costly and it's unlikely they will bother. They might also add you to their black-list of non-payers, which might cause potential issues when booking a hotel in the same country.

However if you do so, you will not be able to book the same room again, as there's a very high chance the hotel will demand payment both for the original booking *and* the new booking. So unless you're really bothered by them lowering your price, I wouldn't attempt changing anything.

Legally speaking the hotel is free to charge you any amount of money, as long as that amount was disclosed beforehand. Likewise I assume you won't agree to give a former employer a refund if they find out you've found a new lower-paying job. A price is a price, regardless of what will happen in the future.