The inflation of the currency is the basis of the rewards pool. It also pays for hosting and some development work.
People who buy HIVE POWER engage in a variety of upvoting dances to get their share of the inflation. HP investors consider their piece of the rewards pool in their investment decisions.
The designers of the platform were hoping that the platform would bring in enough new users to keep the price of HIVE from bottoming out.
The inflation is at a fixed rate. So, it would take an infinite amount of time for the currency to expand to infinity. Sergio quoted the whitepaper which sought a 9.5% inflation rate.
Instead of fighting inflation, people on the platform write posts and comments hoping to get their share of the inflation.
Unfortunately, if the site fails to retain users, then the price of the currency will decrease at a rate faster than the users can harvest the rewards pool.
BTW, you can send HIVE and HBD to 
RE: How does Hive fight against inflation?