Again this depends, you're more describing corporate capitalism, most small businesses don't go through these processes and might become worker coops to survive if can't pay wages or if nobody good enough to take over even if its a profitable and expanding small chain.(speak from personal experience)

Its pretty oversimplized to describe the capital acquistion process, small businesses can last 20 or 30 years without any actual outside investment. Most small businesses dont become corporations that require extensive outside investment because its hard, thus your case is only certain if every small business becomes a corporation through outside investment but it doesnt occur everytime and is only an edge case.