So monetarist economists such as Milton Friedman focus on managing the money supply and lower interest rates as a solution to economic downturn. But what would they do in a recession as the interest rate approaches zero and recognises that monetary policy becomes ineffective? Would they turn to fiscal policy even though they highly oppose government intervention?
An excellent overview of not just monetarist view on this issue but all other mainstream views on monetary policy at zero lower bound (ZLB) can be found in Ullersma (2002) The Zero Lower Bound on Nominal Interest Rates and Monetary Policy Effectiveness: a Survey - which is an excellent literature review on this subject (albeit slightly dated).
In short, under the monetarists view 'true' liquidity trap should not exist. Even though there is zero lower bound monetarists would argue that central banks can still stimulate economy through other transmission channels. For example, Meltzer (1963, 1995, 1999) and Brunner and Meltzer (1968), would argue that central bank can still stimulate the economy through asset purchases with implicit assumption that even when the short-run nominal interest rates are at the zero lower bound, yields on non-monetary assets are not necessarily at their lower bounds.
Bernanke and Gertler (1995) would argue that central banks can stimulate economy also through the credit channel that is not affected by ZLB. Basically this amounts to central bank making sure banks are willing to extend credit as much as possible by providing incentives for them to do so. For example, this is actually being tested in the Europe by ECB through long-term repo operations (LTROS). LTROS is a way how central bank should can borrow money to commercial banks and in theory encourage them to lend more. Furthermore, there is no ZLB when it comes to LTROS as long as central bank is just willing to soak up the losses it makes on such lending (at it can always do that by creating more money). See this article in the Economist that talks about LTROS in greater detail.
Lastly, Milton Friedman himself would probably just suggest that central bank engages in 'helicopter money', that is directly giving money to households/firms in some form (see Friedman (1969) The Optimum Quantity of Money: And Other Essays). Such a direct transfer should in principle 'circumvent' the liquidity trap. However, for many central bankers this would be quite radical as such practice could lead to politicization of central banks (since once people learn they can get 'free money' from central banks there might be political pressures for such transfers even when they are not needed).
However, it is worth while noting that the monetarist view above, while still technically being part of mainstream, is not the predominant view in the macroeconomic profession. The current predominant view on ZLB would be more close to the New Keynesian (NK) view on liquidity trap which in the paper cited above is denoted as the 'Krugman's View'). Under the NK view the above mentioned prescriptions would still be helpful, but insufficient and government spending would still be necessary.
Given that several central banks have negative interest rates today, the idea of ZLB seems clearly flawed, but brings up a useful point: Interest rates also reflect risk as well as value of money. Losing a little bit of money through negative rates can be seen as preferable to losing a lot of money through risky investment, or tying up funds so they can't be used later, at a more productive rate. A negative interest rate is a bit like paying a value contingent fee on a deposit at the bank--paying for the security and convenience of storage. Seems theoretically sound for a central bank to just keep lowering rates (and increasing the fee).
The default assumption has always been that when rates went negative, it's possible to keep things in cash or gold. But both have their own costs associated with storage/security, and with fluctuation in value over time.