Woods:

4. Did Christ pay the debt of sinners? In the Scriptures, and in common discourse, the punishment which sinners deserve is figuratively represented as a debt. “Forgive us our debts;” that is, remit the punishment of our offences. The figure is intelligible and striking. As those who are in debt are held to pay a sum of money to their creditor; so sinners are held to suffer the penalty of the law which they have violated. As the creditor can demand payment of his debtors; so the Lawgiver and Judge can require sinners to suffer merited punishment. Accordingly, when they suffer that punishment, they are represented as paying their debt to God, or to divine justice. But the punishment of penitent sinners is remitted. That is, the same figure of speech being retained, their debt is forgiven. And it is forgiven through the vicarious sufferings of Christ. He paid what God accepted, in lieu of the debt which they owed. From a regard to what he paid, God forgives their debt. Thus he virtually paid their debt. He did that which was accepted in the place of it, that which answered the same purposes, and which secured their forgiveness.

But in regard to this kind of language, which is so frequent in the Scriptures and in religious discourse, we must remember that the language is more or less figurative; and then we must determine the sense of the figure, and the extent of the analogy implied, by the nature of the subject, and by all the instructions which the Scriptures give concerning it. Proceeding in this manner, as we do in all other instances of figurative language, we shall easily avoid the difficulties and mistakes which have been occasioned by carrying the analogy implied in the metaphor to an unwarrantable length. Many of the circumstances which belong to a literal debt or an obligation to pay money, do not belong to a sinner’s obligation to suffer punishment. This obligation is of a moral nature; it arises from the moral conduct of him who is to suffer; it pertains to a moral law and administration, and is directed to moral ends. Who can suppose that a debt of this kind, that is, an obligation to suffer punishment for the violation of a moral law, is attended throughout with the same circumstances with a pecuniary debt? When a man’s pecuniary debt is paid, or when that is done which his creditor accepts in lieu of it, he is no longer liable to be called upon for payment, and it would be unjust and oppressive in his creditor to require payment. But this is not true in regard to the atonement, which does, in a certain sense, pay the debt of sinners. Their ill desert is neither taken away nor diminished. Nor would it be any injustice to them, if God should inflict punishment. This all believers acknowledge and feel. The atonement gives them no personal claim to salvation. They cannot demand it as what is due to them on the ground of justice. They cannot say, they should be treated unjustly, or as they do not deserve, if they should not be saved. The atonement was never designed to put sinners in this condition, and to make salvation a matter of debt to them. God provided the propitiation–that he might be just while he justifies believers; not that he might be obliged in justice to save them, but that he might graciously save them, might save them contrary to their personal desert, and yet do it consistently with the honor of his justice. The death of Christ prepared the way for believing sinners to be pardoned and saved by grace. It was never intended to prepare the way for any to be saved without faith, nor even for believers to be saved in any other way than by the abounding of divine grace.

Thus while I maintain the propriety of freely using the Scripture phraseology which represents our exposure to punishment as a debt, and the propriety also of speaking of Christ as paying or discharging this debt by suffering in our stead, and thus procuring our forgiveness; I maintain that both these representations are metaphorical, and are to be understood with such qualifications as the nature of the subject requires, and that the neglect of these necessary qualifications would lead us, as it has led others, into very pernicious errors.

Leonard Woods, “Lectures,” in The Works of Leonard Woods, (Boston: John P. Jewett & Company, 1851), 2: 474-476.  [Italics original and underlining mine.]