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A constructive trust is an equitable remedy resembling a trust (implied trust) imposed by a court to benefit a party that has been wrongfully deprived of its rights due to either a person obtaining or holding a legal property right which they should not possess due to unjust enrichment or interference, or due to a breach of fiduciary duty, which is intercausative with unjust enrichment and/or property interference. 
In a constructive trust the defendant breaches a duty owed to the plaintiff. The most common such breach is a breach of fiduciary duty, such as when an agent wrongfully obtains or holds property owned by a principal. A controversial example is the case of Attorney-General for Hong Kong v Reid, in which a senior prosecutor took bribes not to prosecute certain offenders. With the bribe money, he purchased property in New Zealand. His employer, the Attorney-General, sought a declaration that the property was held on constructive trust for it, on the basis of breach of fiduciary duty. The Privy Council awarded a constructive trust. The case is different from Regal (Hastings) Ltd v Gulliver, because there was no interference with a profit-making opportunity that properly belonged to the prosecutor.
Being a Privy Council decision, Reid did not overrule the previous decision of the Court of Appeal of England and Wales in Lister v Stubbs which held the opposite, partially because a trust is a very strong remedy that gives proprietary rights to the claimant not enjoyed by the defendant's other creditors. In the event of the defendant's insolvency, the trust assets are untouchable by the general creditors. Supporters of Lister suggested that there was no good reason to put the victim of wrongdoing ahead of other creditors of the estate. There was a tension in English law between Lister and Reid which was highlighted in Sinclair Investments (UK) Ltd v Versailles Trade Finance Ltd. The United Kingdom Supreme Court subsequently overruled Sinclair in FHR European Ventures LLP v Cedar Capital Partners LLC, holding that Lister was no longer good law.
In Foskett v McKeown a trustee used trust money together with some of his own money to purchase a life insurance policy. Then he committed suicide. The insurance company paid out to his family. The defrauded beneficiaries of the trust sought a declaration that the proceeds were held on constructive trust for them. The House of Lords said that the beneficiaries could choose between either: (a) a constructive trust over the proceeds for the proportion of the life insurance payout purchased with their money; or (b) an equitable lien over the fund for the repayment of that amount.
There is controversy as to what the true basis is of this trust. The House of Lords said that it was to vindicate the plaintiffs' original proprietary rights. However, this reasoning has been criticized as tautologous by some scholars who suggest the better basis is unjust enrichment (see below). This is because there must be a reason why a new property right is created (i.e. the trust) and that must be because otherwise the family would be unjustly enriched by receiving the proceeds of the insurance policy purchased with the beneficiaries' money. "Interference with the plaintiff's property" can justify why the plaintiff can get its property back from a thief, but it cannot explain why new rights are generated in property for which the plaintiff's original property is swapped.
In Foskett v McKeown, the plaintiff's original property was an interest in the trust fund. The remedy they obtained was a constructive trust over an insurance payout. It is not obvious why such a new right should be awarded without saying it is to reverse the family's unjust enrichment.
In Chase Manhattan Bank NA v Israel-British Bank (London) Ltd one bank paid another bank a large sum of money by mistake (note that the recipient Bank did not do anything wrong - it just received money not owed to it). Goulding J held that the money was held on (constructive) trust for the first bank. The reasoning, in this case, has been doubted, and in Westdeutsche Landesbank Girozentrale v Islington London Borough Council the House of Lords distanced itself from the idea that unjust enrichment raises trusts in the claimant's favour. This remains an area of intense controversy.
These type of trusts are called '"institutional" constructive trusts'. They arise the moment the relevant conduct (breach of duty, unjust enrichment etc.) occurs. They can be contrasted with '"remedial" constructive trusts', which arise on the date of judgment as a remedy awarded by the court to do justice in the particular case.
An example is the Australian case Muschinski v Dodds. A de facto couple lived in a house owned by the man. They agreed to make improvements to the property by building pottery shed for the woman to do arts and crafts work in. The woman paid for part of this. They then broke up. The High Court held that the man held the property on constructive trust for himself and the woman in the proportions in which they had contributed to the improvements to the land. This trust did not arise the moment the woman commenced improvements - that conduct did not involve a breach of duty or an unjust enrichment etc. The trust arose at the date of judgment, to do justice in the case.
In Bathurst City Council v PWC Properties, the High Court that as constructive trusts are the most severe remedy in cases of breach of fiduciary duty, they should only be imposed when other remedies are inappropriate in providing relief.
For example, if the defendant steals $100,000 from the plaintiff and uses that money to buy a house, the court can trace the house back to the plaintiff's money and deem the house to be held in trust for the plaintiff. The defendant must then convey title to the house to the plaintiff, even if rising property values had appreciated the value of the house to $120,000 by the time the transaction occurred. If the value of the house had instead depreciated to $80,000, the plaintiff could demand a remedy at law (money damages equal to the amount stolen) instead of an equitable remedy.
The situation would be different if the defendant had mixed his own property with that of the plaintiff, for example, adding $50,000 of his own money to the $100,000 stolen from the plaintiff and buying a $150,000 house or using plaintiff's $100,000 to add a room to defendant's existing house. The constructive trust would still be available but in proportion to the contributions, not wholly in the claimant's favour. Alternatively, the claimant could elect for an equitable lien instead, which is like a mortgage over the asset to secure repayment.
Because a constructive trust is an equitable device, the defendant can raise all of the available equitable defenses against it, including unclean hands, laches, detrimental reliance, and undue hardship.