There will be the same number of HBD/HIVE as before. The difference is the HBD is being placed in the wallets of individuals and not in the DHF.

This is sort of true, in that nothing changes at the moment of the trade. But the HBD being sold by the stabilizer comes from the DHF, where it counts toward the supply but not toward the debt ratio. The HIVE that the stabilizer accumulates selling HBD is sent back to DHF where it is converted into more HBD. So the net effect is an increase in HBD i.e. increase in supply, and decrease in HIVE (since the HIVE is destroyed when DHF converts it into HBD).

This is ultimately how the stabilizer "stabilizes" HBD (on the up side). When HBD is overvalued, it uses the DHF to create more, satisfying demand. The mechanism works similarly in reverse when HBD is undervalued.

If people want to increase HBD supply, they need to be willing to overvalue it a bit, so the stabilizer pushes back by creating more. The high APR offered (both on chain and from the liquidity pool) provides a motivation to overvalue it.