The logic of austerity is based on the theory of the firm, which is that if it is in trouble a firm can get rid of costs (like employees) without worrying about them after they leave as they are no longer on its payroll. But this is not of course true of the state: if someone is made unemployed in the state and there is no alternative work for them they still exist: they still have to be fed, and they still need public services. All that happen is that as a result of their sacking there is now no productive activity from them to help meet that demand, or pay the tax that makes it possible. So, in the economy as a whole sacking people simply means that there is less income and if there is less income than it inevitably follows there is less tax, more benefits are paid, and the pressure on public services is therefore greater, and the capacity to supply such services is reduced.
Thus the government borrows more money and this is fiscal stimulus. “Automatic stabilisers” in the jargon.