I was reading a history book on the Russian revolution that claimed that many Imperial Russian soldiers didn't have rifles, and were forced to pick up the rifles of their fallen comrades. I've heard similar debunked claims regarding the Red Army in WW2. Did the Imperial Russian Army really face such significant equipment shortages in the Great War, or is it largely a myth?
It's true...for certain years of the war (mostly late 1914 to late 1915). During WWI, patronnyy golod, or “cartridge hunger" was a serious issue for Tsarist troops, who sometimes had to resort to bayonets when the ammunition ran out. Rifle shortages also occurred and there were allegedly a few cases where unarmed troops were sent onto battlefields to scavenge for rifles and ammunition.
There are a handful documented cases of "two men, one rifle" during WWII. However, the Enemy at the Gates depiction of the Red Army doing this at Stalingrad is wildly misleading. In fact, some of the better-documented cases of "two men, one rifle" happened near Leningrad and mostly involved citizen militias, rather than Red Army forces.
Sending unarmed men into battle wasn't Red Army doctrine, so when this id occur it was usually because the situation was desperate (underarmed troops encircled during Barbarossa trying to break out, etc.)
I've written a ton about Russian supply issues in WWI and the "two men, one rifle" myth in another post that you may find interesting!