The system funds itself by directing a percentage of new supply created into the buffer. In the case of an oversupply due to dropping demand, the system burns currency from the buffer. Should the trend reverse and there be a supply deficit once more, it will receive its percentage of new supply once again. Rinse...repeat. (this was omitted from the Bitcoin simulation to ensure it was more in line with Bitcoins behaviour)
Burning currency from the buffer will have no impact on price. Despite the quantity theory of money, people don't respond to changes in supply, they respond to changes in the order book.
The only way to change the buy-side of the order book is offer interest for term deposits. Even this is limited because after a while no amount of interest will generate demand.
Assuming you have a reliable price feed there are better alternatives to maintaining a stable value.