For simplicity, ignore government spending and taxes. "Fiscal policy" means lump-sum transfer payments.

Suppose the economy is in a permanent liquidity trap. If we ignore the central bank's paper and ink operating costs, another name for the permanent liquidity trap is the "Friedman Rule". Both have the nominal interest rate on bonds at 0%, so that currency is not scarce relative to bonds. If it follows the Friedman Rule, the central bank earns zero seigniorage profits. Because seigniorage profits are equal to the interest earned on the bonds that are on the asset side of the central bank's balance sheet.

If the economy escapes the liquidity trap (violates the Friedman Rule), so the nominal interest rate on bonds becomes strictly positive, then the central bank will earn strictly positive seigniorage profits. If the government owns the central bank, the central bank will give those seigniorage profits to the government. The long run government budget constraint tells us that this must increase the present value of government transfer payments. But that means a change in fiscal policy.

Therefore the only way the economy can escape a permanent liquidity trap is if fiscal policy changes.

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