The whole idea was derived from a novel called The Moon is Down by John Steinbeck, in which the people of an occupied nation freed themselves after their alllies dropped explosives to them. The idea was taken up by something called the Joint Psychological Warfare Committee, one of the many organizations doing that kind of thing, mostly under the impression that the war could be won without messy things like dead Americans.
The Moon is Down was mostly moonshine, as any real psychologist could have told them. In an occupied country, most people hunker down and hope just to stay alive; only a very few will fight, considering the great risk, not just to themselves but to the community. (The Germans reacted to an attack on them by randomly executing inhabitants of the nearest town, a high price to pay for killing one German.) Dropping tons of little pistols in the hopes that a French housewife would find one and be transformed into an avenging Jeanne d'Arc, slaying les Boches right and left, was a pipe dream.
Realizing the improbability of the whole concept, theater commanders made no use of the "Liberator" and they stayed in depots until the end of the war, when they were dumped in the ocean. A few were used in the Pacific area, after the war, to arm some police until better weapons could be obtained, but reports of use against any enemy seem to lack confirmation.
In the real world, the allies (mainly the British) dropped real weapons to known resistance groups. Common small arms were STENs, PIATs, Enfield revolvers, and SMLE or No. 4 rifles. U.S. carbines and some M3 SMGs were also dropped; all by parachute. NO Liberators were dropped, with or without parachutes.
Jim