The Government taking money and burning it is called "taxation". With fiat currency, the government makes the money, out of nothing, at its discretion. They then collect most of it back in the form of taxes. Keep in mind, the money they're collecting is going into the pile of infinite money, and Inf + 1 = Inf.

Fiscal policy all about adjusting those levers (how much, and where, the government injects money into the economy, and how much, and where, the government extracts it back out) in order to promote the society we want to have.