Max subsidy is a feature made for controlling the inflation of a coin.
According to Tranz, the HBN/CAP developer:
The main reason for max subsidy is to incentive people to stake on a daily basis rather then only a few times with large blocks. Mostly it would be to prevent someone from simply holding thousands of coins offline, and then bring them back online after a long time and get a very large reward, for doing almost no network protection.
It first appeared with NovaCoin, where it was used in conjunction with NVCS (the NoVaCoin Stake algorithm, also called dynamic interest rate, where the interest rate decreases as more coins are staking). The purpose of max subsidy in coins like NVC and CAP is about preventing abuse of long term holders bringing old coins online and shocking the money supply.
Unlike previous coins, HyperStake uses the maximum stake reward as its primary means of controlling inflation (there is no NVCS in HyperStake). HyperStake allows a maximum of 1,000 HYP to be staked in one block (not per address).
Max subsidy works in this way: it places an upper limit to the amount of reward one gets when staking. For instance, if the block size is large enough to provide a 1,200 HYP stake reward the maximum reward will be triggered, and the extra 200 HYP are not rewarded - they are "lost" for the holder. In order to avoid losing potential gain, the HYP holder is encouraged to reduce the block size of each block so that the reward is less likely to hit the cap. This means that instead of one block, now there will be two or three smaller blocks, which means more blocks securing the network with their stake weight.
Another way to explain max subsidy:
The point of it is to economically encourage security. Without a max subsidy, you could have one block of 100k HYP, open your wallet after 8.73 days and in the minute you would get your reward (with such a mammoth block, you'll be pretty sure to be the first to stake when you enter the contest). So you would not be spending time with your wallet open to secure the network.
Lack of max subsidy is the code equivalent of "whether I work or not, I get paid the same".
Max subsidy has two useful consequences: blockquote encourages everyone to have smaller blocks so pretty quickly, there is a lot of competition for staking, so one need to leave one's wallet open more often to have a chance to stake.
smaller blocks means more blocks, which means more staking periods. In the end, one spends much more time securing the network. Remember: one doesn't get BTC as a courtesy. One gets BTC as an incentive to secure the network. The BTC one gets is just a "thank you" for securing the network, not the other around. Same with PoS.
Implementing max subsidy has the added effect of reducing compounded interest because each block will take longer to stake.
Contrary to NVCS where the interest rate decreases with time, with HyperStake the interest rate always stays the same, 750%. Inflation is further limited by another factor, max generation.