Hive inflation is reduced every 250k blocks or so, depending on what HBD does to it over the years and at which supply we'll end up with once we hit 0.5% yearly inflation it's going to remain at 0.5%.
Say for instance in 13-14 years when we're at 0.5%, currently I believe we're at 12% or so (Curation + vests inflation), we land on 1 billion Hive tokens in existence, then there'll only be 5 million new Hive yearly. If we then have 10 million active daily users rather than current 10-20k, it'll mean that those ~14k daily Hive will be quite hard to attain "from scratch", especially since 50% of those will go to curators, i.e. those already holding Hive Power. Split even more to reward the DHF and witnesses as it is currently.
Either way, inflation is being reduced and I suppose if that 0.5% means 0.5% yearly at current supply, that means that each year after the first 20 years of the chain it'll start going up slowly again, cause 0.5% of 1B tokens is 5M, but 0.5% of 1.05B tokens is 5.25M in (year 22 of Hive), etc. (But it could also be that 0.5% means 0.5% after 20 years, thus only constant 5M tokens per year, not growing.
There's some activity to help maintain the peg currently but it's going to help a lot more to give HBD usecases, people being interested in holding and using it and making sure the peg stays at $1, more exchanges listing HBD and causing traders to arbitrage it between exchanges and the inner market, etc. It is also capped where if the price of Hive goes low enough then HBD stops printing - and witnesses can also adjust the APR the HBD in savings gives if they deem it necessary, so the same thing that happened to Luna can't happen here, it won't affect the supply of Hive.