Maybe you're specifically thinking of Communist Russia which allowed for small businesses to have private ownership, or perhaps you're thinking of Anarcho-Communism?

But the reality is, private ownership is the antithesis of collective ownership, so most socialists aren't really on board with that.

Via Wikipedia, which makes the point numerous times, with a plethora of scholarly references:

https://en.wikipedia.org/wiki/Socialism

Socialists view private property relations as limiting the potential of productive forces in the economy. According to socialists, private property becomes obsolete when it concentrates into centralised, socialised institutions based on private appropriation of revenue—but based on cooperative work and internal planning in allocation of inputs—until the role of the capitalist becomes redundant. With no need for capital accumulation and a class of owners, private property in the means of production is perceived as being an outdated form of economic organisation that should be replaced by a free association of individuals based on public or common ownership of these socialised assets. Private ownership imposes constraints on planning, leading to uncoordinated economic decisions that result in business fluctuations, unemployment and a tremendous waste of material resources during crisis of overproduction.

But don't worry, I fully expect a response that keeps arguing the same thing with no evidence to support it. That's what I usually get here, it's like the world has become illiterate.