Nothing. Rules remain the same for the protocol. Only parameter altered is block reward, that will be 0 once the last one is mined
actually a lot of things will happen because of that!
those altcoins that are relying on the distribution model of bitcoin, which is creation of new tokens in form of block reward given to the miners which then sell it to the market, has so far died before they reach their final stage of even nearing maximum supply let alone reach it.
and there is a good chance that the rest which are not close to that date will die badly because as the difficulty rises or the mining reward lowers and as the price of altcoins drop over time, mining becomes less profitable and because of that miners will stop mining and leave the network open to attacks.
if you check out some of the old nearly dying altcoins you can see many of them are attacked every now and then because their network is weak now.