As you may already know, economies e.g., go through "business" cycles, which results in boom periods and bust periods. In booms, unemployment is low, but there are inflationary pressures. In busts, inflation is low, but unemployment is high. Stabilization policy is designed to smooth things out; make the highs not so high and the lows not so low.
Im not sure what you are looking for in what cannot be stabilized. Is it something like the weather? Or is it something where one type of stabilization doesnt work.
One stabilization policy in bust times is to increase the money supply. However, as Keynes argued, if the economy is in a "liquidity trap", no amount of monetary policy could be used to increase economic activity. Fiscal policy was the solution.