When the price of HBD deviates from $1, the stabilizer buys or sells HBD to push the price back to $1. This doesn't happen instantly because the stabilizer has a limited budget (currently about 7000 HBD per hour), so it may take time to buy or sell enough HBD to restore the peg. That's why there have been some temporary periods that the price may deviate, including recently when HBD went to about $3 and took about two days to get back to $1.