Capitalists cease to exist and workers cease to be their employees. Ownership by workers of necessity has to be collective ownership by society as a whole. Modern means of production cannot be divided up among workers like the hand tools of old. They have to be owned and used in common. However, if they were, the level of ownership of each worker would be considerably constrained.
Social ownership is central to removing the shackles that hold back the economy under capitalism.
Society can now control the economy and be free of the anarchy of capitalism. And production is aimed at maximising the satisfaction of human needs rather than the profits of capitalists. In another sense socialist ownership is highly individual. Collective ownership is not ownership by 'the collective', it is joint ownership by individual co-owners. This is reflected in the fundamental change in the position of the worker.