Earlier quoted context omitted.
Well, of course it's easy to ensure that the price doesn't stay above $1. You can make more of them. It's ensuring that the price doesn't stay below $1 that's hard. You have to draw value from some reserve. If that reserve is depleted, you're screwed. All attempts to peg currencies run into that problem.
Would it not be possible to just destroy some of the coins? If they were destroyed for everyone, proportionally to how much they hold, wouldn't that be in interest of everyone? Because it would make the coin itself worth more?
The first is distributed destruction. Everyone destroys some of their coins to raise the value of remaining coins. The problem is that this is a prisoner's dilemma: defection is the best strategy. Some people will not destroy their coins, thus increasing their relative position to others who do. Over time "destroy your coin" signals will simply be ignored.
Not to mention cold wallets, which simply don't participate in the ledger unless it suits them to. Are they meant to simply nuke coins upon rejoining? This introduces an incentive to stockpile coins in the hope that the policy will change in future.
The second approach is centralised. Someone has the authority to mark some fraction of coins as destroyed. Rather undermines the decentralisation thing people like.