Different socialist and communist communities interpret this differently. The fundamental baseline is no one should starve, no one should be homeless, no one should lack basic medical care -- essentially there should be a baseline safety net for everyone.
Some communities focus on workers and profit distribution - the company's profit should be directed by the workers, reinvested or paid out at their discretion (rather than collecting in the pocket of "owners"). Some focus on equality of outcome. Some are built of gift economies similar to the economies of some indigenous tribes.
What most people think of as communist is the Stalinist model of the Soviet Union - an authoritarian, single party, fairly corrupt institution. The Soviets pushed their brand of communism onto other countries, which is why you see so many built on that model. (The Soviets actually attacked other communist states that were more libertarian and democratic.)
I would say yes, authoritarian communism is prone to the outcomes you describe. There's a reason I disparage Stalinists by calling them "Tankies" and do my best not to associate with them.