The stabilizer gets post rewards. You can support it that way by voting for the daily comments posted by hbd.funder
It doesn't really need a source of funding. The stable coin works to some extent even without a stabilizer but it has more short term swings. But even if you wanted a stabilizer, it could work fine with just a fixed pool of capital, and no ongoing funding. Historically the stabilizer has turned a profit and it probably would in the future as well, but even if not it could still work as long as it didn't lose so much that it ran out of capital to trade, which is very unlikely.
RE: HBD Stabilizer - Renewal R4-2025