In each case, because I-X pays money to X which otherwise D would have had to pay, the law permits I-X to enforce X's rights against D to recover some or all of what I-X has paid out. A very simple (and common) example of subrogation would be as follows:
If X were paid in full by I-X and still had a claim in full against D, then X could recover "twice" for the same loss. The basis of the law of subrogation is that when I-X agrees to indemnify X against a certain loss, then X "shall be fully indemnified, but never more than fully indemnified ... if ever a proposition was brought forward which is at variance with it, that is to say, which will prevent [X] from obtaining a full indemnity, or which will give to [X] more than a full indemnity, that proposition must certainly be wrong.
I-X will normally (but not always) have to bring the claim in the name of X. Accordingly, in situations where subrogation rights are likely to arise within the scope of a contract (i.e. in an indemnity insurance policy) it is quite common for the contract to provide that X, as subrogor, will provide all necessary cooperation to I-X in bringing the claim.
Subrogation is an equitable remedy and is subject to all the usual limitations which apply to equitable remedies.
Although the basic concept is relatively straightforward, subrogation is considered to be a highly technical area of the law.
It is periodically argued that the concept of unjust enrichment provides the conceptual underpinning for the law of subrogation. Whilst this is probably true as a matter of the English language (otherwise X could be paid twice in respect of the same claim), other academic commentators have disagreed that subrogation fits squarely with accepted legal reasoning relating to this field. In reality, the argument as to the conceptual underpinning for the legal technique is more theoretical than practical.
There is also lively debate in legal circles as to whether the rights of subrogation are the subject of an express or implied agreement, or whether they arise automatically by operation of law. The reasoning of the courts has not always been clear in relation to this, but the answer is probably all three in many cases. It is clear that subrogation rights can arise even where there is no contract between subrogor and subrogee, so it is clearly not necessary for there to be an express or implied term. However, it clearly is an implied term of any policy of insurance or guarantee that the insurer or guarantor will be subrogated in the event of any payment by the insurer to the insured party. However, in practice, most policies of insurance will contain an express clause regulating subrogation rights as well.
Although the classes of subrogation rights are not fixed (or closed), types of subrogation are normally divided into the following categories:
Although the various fields have the same conceptual underpinnings, there are subtle distinctions between them in relation to the application of the law of subrogation.
An indemnity insurer in fact has two distinct types of subrogation right. Firstly, they have the classic type of subrogation used in the example above; viz. the insurer is entitled to take over the remedies of the insured against another party in order to recover the sums paid out by the insurer to the insured and by which the insured would otherwise be overcompensated. Secondly, the insurer is entitled to recover from the insured up to the amount which the insurer has paid to the insured and by which the insured is overcompensated. The latter situation might arise if, for example, an insured claimed in full under the policy, but then started proceedings anyhow against the tortfeasor, and recovered substantial damages.
A surety who pays off the debts of another party is subrogated to the creditor's former claims and remedies against the debtor to recover the sum paid. This would include the endorser on a bill of exchange.
In relation to a surety's subrogation rights, the surety will also have the benefit of any security interest in favour of the creditor for the original debt. Conceptually this is an important point, as the subrogee will take the subrogor's security rights by operation of law, even if the subrogee had been unaware of them. Accordingly, in this area of the law at least, it is conceptually improbable that the right of subrogation is based upon any implied term.
A trustee of a trust who enters into transactions for the benefit of the beneficiaries of the trust is generally entitled to be indemnified by the beneficiaries for personal loss incurred, and has lien over the trust assets to secure compensation. If, for example, the trustee conducts business on behalf of the trust and fails to pay creditors, then the creditors are entitled to be subrogated to the personal and proprietary remedies of the trustee against the beneficiaries and the trust fund. Where under the terms of the trust instrument the trustees are permitted to trade in derivatives as part of the trust's investment strategy, then the derivatives document will also normally contain a subrogation clause to bolster the common law rights.
Where a lender lends money to a borrower to discharge the borrower's debt to a third party (or which the lender pays directly to the third party to discharge the debt), the lender is subrogated to the third party's former remedies against the borrower to the extent of the debt discharged.
However, if the original loan was invalid (because, for example, it was ultra vires the borrower) then the lender generally cannot enforce the third party's claim against the borrower as this would indirectly validate an invalid loan. Nonetheless the claim can subsist insofar as the unlawfully borrowed money was used to discharge lawful debts, by inferring the legality of the use of the funds to the right of subrogation. The law in this area has been subject to conflicting decisions.
Where a bank, acting on what it believes erroneously to be the valid mandate of its client, pays money to a third party which discharges the customer's liability to the third party, the bank is subrogated to the third party's former remedies against the customer.
In Lord Napier & Etterick v Hunter  2 WLR 42, the House of Lords confirmed that an indemnity insurer's subrogation rights against the assured are not limited to a simple personal remedy; the insurer also has the benefit of an equitable lien over the damages received by the assured. That case also controversially held that in working out the overcompensation to which the insurer is entitled the assured cannot first recover the whole of his uninsured loss, and must instead bear the excess agreed.
Subrogation can thus be in conflict with Make Whole Doctrine, the right of an injured party to recover full damages. This abrogation of Make Whole doctrine puts the insurer in the position of having first claim to an at-fault party's assets, even if the assured is left destitute as a result (see Northern Buckeye vs Lawson - 2004). In other words, the law's intent to prevent dual recovery by the assured can lead to less-than-equitable recovery.
In the cited case, the Ohio Supreme Court ruled that the language of the assured's insurance contract overruled Ohio's statutory default Make-Whole Doctrine. For this reason, an insured client needs a full awareness of subrogation clauses in his insurance contracts, including insurance provided by employers, fraternal organizations, etc.