There is no HDB in an interest bearing account having to do with the stabilizer. The stabilizer receives it, converts it if appropriate, uses it for trading if appropriate, and then sends it back when the price does not provide any opportunity to exchange or trade. Nothing is held.
Opinions obviously differ on the merits of voting for hbd.funder comments vs other posts. I'm not going to try to convince you. I don't think it was was my idea, but I don't entirely remember.