Without getting into too much detail and jeopardizing our IP, there are a number of ways to reduce the supply without hair cutting wallets (which would be a TERRIBLE solution!!).
Most obvious is to burn fees instead of passing them on as earnings to network nodes. Transactional and general usage fees are the first port of call, followed by DEX trading fees. These mechanisms are sufficient for small adjustments but don't offer a huge amount of supply reduction capability in the event of a "crash".
The main mechanism is provided by the fact that to stabilize the base currency independent of oracles and pegging, is that the system itself mediates a lot of the trades. Therefore if a lot of people are cashing out to USD for example, the Radix tokens can be burnt (publicly thus auditable) by the system in order to reduce the available supply and return confidence to the price.
After thinking about this for a long time, I came to the conclusion that any burning of coins is unnecessary. It punishes people who are actively using the currency (and possibly those protecting it if tx fees are not increased to compensate) in favor of those who are most likely just speculating. In any currency where the price has the ability to remain relatively stable, it should be much less likely that the price is scaring/encouraging people into selling, so the mechanic is likely trying to fix something that isn't broken.
Just my two cents.