An example is the United States after the 2007–09 crisis: easy monetary policy cushioned the economy and also helped heal a broken financial system. In both of these cases, there is no trade-off for monetary policy. There are other situations, however, where there could be tension between the two objectives.
It should, however, be noted that within the euro area there has certainly been a differentiation among different government bonds: while German Bunds have generally remained quite liquid, the liquidity of bonds issued by countries with weaker public finances, such as Italy and Greece, has at certain point in time been heavily impaired.