The final clause of the 5th Amendment to the United States Constitution state "nor shall private property be taken for public use without just compensation."
The principal application of this clause has been to compel government to pay a fair price for property taken by eminent domain to build public works like highways. But, there is a fair reading of the clause which could have broad application in the criminal justice context by protecting the rights of the innocent.
The status quo is that if the police and prosecutors and courts follow the proper procedure and have probable cause to believe that you committed a crime, that the government has no responsibility to compensate you in any way for your troubles, even if you have not, in fact, committed any crime. A handful of states, Florida prominently among them, but only a handful, reimburse you for your attorneys' fees if you retain a private attorney and are acquitted at trial. Most states provides a pittance of compensation for people who are convicted of a crime and imprisoned for years, only to latter have the conviction be set aside on the basis of actual innocent (e.g. DNA evidence). I'm not aware of any state that compensates people who are arrested or subjected to a search conducted in a "reasonable" manner based on probable cause, even if the arrest turns out to be a the wrong person, or the search proves fruitless. Federal law does not require someone who is accidentally harmed by the police when acting in good faith to be compensated -- civil rights claims require proof of an intent to violate a constitutional right and may be asserted only against the person who actually did so unless a right was violated pursuant to a governmental policy.
If the definition of private property is read broadly, however, to include your right to sell your services to others or use your time for leisure, then the resolution of all of the above cases would be different. Even if due process is provided, just compensation must be provided for those who are innocent. Every acquitted individual would have a right to compensation for their attorneys' fees and for any time spent incarcerated pending trial. Every innocent person convicted of a crime, even with all procedural regularity, would have a constitutional right to just compensation. Every person arrested but not guilty, and every person subjected to a fruitless search, likewise, would be entitled to some compensation for the modest inconvenience -- perhaps a couple of days in jail or time spend enduring the search. Every person justifiably killed by a policeman who in good faith believed you were pointing a gun at him, when that person was really just holding a can of soda, would be entitled to compensation for the death, regardless of the policeman's good intentions.
Likewise, innocent citizens compelled to serve their government through jury duty or a military draft, would have a more compelling claim to just compensation, rather than merely the amount that the state deems fit to make available without regard to any constitutional limitation. Certainly, requiring jurors to serve for less than the minimum wage, a common practice now, would be unconstitutional.
The Third Amendment takes a similar approach to the Fifth Amendment takings clause, suggesting that this a broad reading of the takings clause in criminal justice settings would not do great injury to the Founder's intent in this area.
A takings clause approach to compensating the innocent would also, as is the case in eminent domain cases, place liability on the governmental entity on whose behalf the offending act was taken, rather than the often judgment proof individual who actually did it, who may also be difficult or impossible to identify by name (hence the common practice of policemen putting black tape over their names on their badges to make them harder to sue). Individual offenders would still be liable for intentional violations of constitutional rights, but this would generally be in addition to, rather than instead of, a takings clause remedy.
The existence of a no fault compensatory remedy from a solvent entity for innocent people harmed by the criminal justice system would go a long way towards defusing the fierce tensions between citizens and law enforcement common in much of the United States, particularly across race lines. The no fault nature of the remedy would save face for law enforcement and discourage dishonesty by police trying to concoct probable cause justifications after the fact.
A strong takings remedy might also open the door to reconsidering a legal stance that police hate, the 4th Amendment exclusionary rule, or at least, modifying it in application. For example, if there was a strong civil takings remedy, it might make more sense to eliminate the exclusionary rule for physical evidence obtained in a search, limiting the remedy for a 4th Amendment violation to a civil suit claiming a taking (if the search was fruitless) and to a civil rights suit (whether the search was fruitful or not). Moreover, in the civil rights suit, in a case where the search did produce contraband or evidence, there might be a presumption that would have to be overcome, perhaps even by clear and convincing evidence, that probable cause for the search did exist. This kind of presumption makes sense because many police with "hunches" that don't count as probable cause that make searches that produce evidence are simply inarticulate when it comes to explaining why they had probable cause, rather than actually lacking in probable cause.
This kind of takings clause jurisprudence would be a stark departure from existing law, but it would hardly be radical, and would create a strong incentive to exercise caution towards people who are likely to be innocent. A takings clause approach would restore a focus on the importance of actual guilt or innocence that our elaborate habeas corpus and 4th and 5th and 6th Amendment jurisprudence has diverted attention from in the criminal justice system. Many observers have noted the undue importance the American system of criminal justice places on process over the merits, to the point where it isn't even entirely clear that actual innocence is a valid ground to collaterally attack a procedurally sound order to execute someone.
Exclusionary rule reform and this takings jurisdiction, as a package, would make justice more certain for people we know are factually guilty, while more directly addressing the rights of the innocent that the exclusionary rule is supposed to condition law enforcement officers to respect. As it is, a law enforcement officer who can articulate probable cause, even if he doesn't actually believe it, can harass the innocent with impunity, a serious flaw in existing law that breeds distrust between police and citizens.
This also doesn't have to bankrupt the government as it tries to enforce the law.
Acquittals are rare, making up only a couple of few percent of all criminal cases prosecuted, and most acquittals come in cases where there was very little pre-trial detention that must be compensated, since the defendant was released on bond, and where the defense has already been paid for because the defendant had a public defender.
The number of convictions overturned on any reason is a tiny percentage of the total, and often even when convictions are overturned, this happens before a sentence on other convictions which are not overturned is complete.
The number of people who die in custody (other than from old age) or at the hands of police for any reason is on the order of one per three million people each year. A large percentage of those deaths are justifiable homicides of guilty people committing crimes, not mistakes.
There are lots of fruitless searches conducted each year, and there are lots of arrests that don't produce criminal charges each year. But, fair compensation for these kinds of events wouldn't have to be huge -- perhaps $20 an hour (about the median hourly wage), with a minimum compensation of $10, in an ordinary case. Most fruitless searches would put the police out $10-$20 if nothing was damaged in the process. A wrongful arrest, such as one involving a mistaken identity, might usually call for compensation under $1,000, depending on how long it took to resolve.
It would cost something, there is no doubt, but the incentive this scheme would create to engage in targetted policing might be worth the trouble. And, many people impacted by the criminal justice system might choose to forego bringing a civil rights suit when they could far more easily prove a taking and secure compensatory damages, so it might actually reduce the cost to governments of civil rights suits, effectively shifting money from paying lawyers to paying citizens who have been inconvenienced.