How did 'equity' semantically shift to mean 'Assets — Liabilities'?

Solution 1:

Once upon a time, the word law stood for a system of rules that were very rigid and that the courts were obliged to enforce very rigidly. That system of rigidly enforced rigid rules often produced results that were harsh and intuitively unfair, and so there emerged a system of rules, practices, and the institutions, whose aim was to correct the harshness of the law, in that narrow sense, and produce the results that were closer to what seemed intuitively just. That system was called equity. (See the quotation in the WS2’s answer for a more formal statement of this.) In the terminology of the time, the law and equity thus stood in contrast to each other.

Over time, the two systems merged, and what most of us, in most contexts, nowadays call the law encompasses both the elements that have their origins in the law in that narrow sense, and the elements that have their origins in equity. There are, however, in the present-day law (in the broad sense) still numerous echos of the distinction between the law, in the old, narrow sense, and equity. In the context of legal practice, the word law continues to sometimes be used in the narrow sense, in which it is contrasted with equity.

What is crucial to understanding the shift that the question is about is that under the rules of the law, in that narrow sense, the mortgagee (the lender, e.g. a bank) holds the title to the property (i.e. is its owner), until the last penny of the debt is repaid; it is only then that the buyer becomes the owner. You could thus repay 99% of the debt, and still own nothing, in the eyes of the law, in the narrow, old sense. If the law, in that sense, controlled the outcomes, that would, of course, often produce harsh, unjust results. To prevent such injustices, the rules of equity emerged that treat the mortgagor as, in a way, owning something even before the debt is fully repaid. The word equity came to be used for what the mortgagor has, because his having it depended on the rules of equity.

Solution 2:

It is Sense 5 of the word equity in the OED.

The earlier senses relate to the notion of equity as an adjunct to law, and forming an essential part of jurisprudence in all English-speaking jusrisdictions. Sense 4a has relevance.

4a. In England (hence in Ireland and the United States), the distinctive name of a system of law existing side by side with the common and statute law (together called ‘law’ in a narrower sense), and superseding these, when they conflict with it. The original notion was that of sense 3, a decision ‘in equity’ being understood to be one given in accordance with natural justice, in a case for which the law did not provide adequate remedy, or in which its operation would have been unfair. These decisions, however, were taken as precedents, and thus ‘equity’ early became an organized system of rules, not less definite and rigid than those of ‘law’; though the older notion long continued to survive in the language of legal writers, and to some extent to influence the practice of equity judges. In England, equity was formerly administered by a special class of tribunals, of which the Court of Chancery was chief; but since 1873 all the branches of the High Court administer both ‘law’ and ‘equity’, it being provided that where the two differ, the rules of equity are to be followed. Nevertheless, the class of cases formerly dealt with by the Court of Chancery are still reserved to the Chancery Division of the High Court.

Following this principle - sense 5b relates the system of equity to a mortgagor.

5b. equity of redemption: the right which a mortgagor who has in law forfeited his estate has of redeeming it within a reasonable time by payment of the principal and interest. equity to a settlement: a wife's equitable right to have settled upon her any properties coming to her after marriage.

The foregoing is the history of the way in which the jurisprudential concept of equity became applied to the notion of ownership. A relevant example of its use is from 1966 and the Dictionary of Economic Terms:

1966 A. Gilpin Dict. Econ. Terms (1967) 72 Equities, the ordinary shares of a limited company. They carry the right to the residue of a company's assets after it has paid all its creditors, and share in the distribution of profits, if any, after interest has been paid to preference share-holders and debenture holders each year.