In a society where slavery and indentured servitude are not legally enforceable, no-one can own a firm because a firm is a set of human agents. It is of course possible for someone to own an asset used by a firm, to own a claim on the net income from the firm's activities, to control the allocation of resources trough the firm's governance structure, or even to own a controlling position within this governance structure. But the human beings constituting a firm cannot be bought and sold.Obviously these points are made in the context of a book advocating an increase in employee control of firms, but they seem pretty sound to me.
As everyday common sense suggests, firms are organisations consisting of people. The firm called General Motors includes employees of GM. There is an ultimate control group for GM - namely, its shareholders. But when someone buys a share (or even a majority of shares) in GM on the stockmarket, they are not "buying the firm." Rather they are buying a role or position in the firm, the role of being a GM shareholder. This role is defined by a bundle of rights including the right to receive dividends, the right to a share of GM's assets if they are liquidated, and the right to vote at shareholder meetings. Such roles can most certainly be treated as commodities and passed from one person to another. But the firm is not bought or sold in the process, because it is larger than its shareholders.
It also points up the reason why shareholders, particularly of companies that rely heavily on skilled employees, ought to be concerned about (hate the term) 'human capital'. Arguably the only evidence we see of this is in the banking sector where some shareholders have pushed for banks to keep up pay levels and hang onto key staff even if they bear some responsibility for poor behaviour. But maybe the fact that it's an exceptional case demonstrates that asset managers only rely grasp the importance of human capital in their own backyard. But if companies lose their skilled employees (perhaps in no small part due to a change in 'ownership') then the real firm is reduced even if the thing that shareholders own - control rights over the firm - is unchanged.