If you are looking for an absolute stability this can only happen in a situation at which an asset can only be traded with you but not between third parties; then the value you set would be definite.
However as long as third parties can trade with each other, the value becomes variable. This poses a challenge for currencies because a healthy economy needs a relatively stable currency. There are certain methods to succeed this. The primary method is holding large amount of any currency in a limited number of private or public funds which create stabilization by initiating buy/sell actions against the trend. These funds doesn't need to hold a large percentage of the currency as one might imagine. Something like 5-10% would be more than enough. No one actually holds 100% backup to stabilize the pair. That is just an empty promise by Bitfinex to assure people, the company is no way near that big to afford locking up that much money. If they would have to buy all the Tether, they would file bankruptcy and disappear long before they let out a penny. Financial institutions always do this and it always burns the small investors the most.