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Because the finding has been done by a government employee, the law that applies is the Constitution rather than theft laws. If a police officer, park gardener or other public worker comes upon bags full of objects, bedding, cooking supplies, or anything else, looks through those possessions, and then takes them away, it might be an illegal search and seizure under the Fourth Amendment of the U.S. Constitution. 
The Fourth Amendment declares that “The right of the people to be secure in their persons, houses, papers, and effects, against unreasonable searches and seizures, shall not be violated…”  Because it goes on to state that “no warrants shall issue, but upon probable cause, supported by Oath or affirmation, and particularly describing the place to be searched, and the persons or things to be seized” this clause has long been understood to mean that when they are investigating a crime, the police have to obtain a warrant from a judge before searching through people’s property and seizing any of it to use as evidence in a criminal trial. But it also applies when police are not investigating crimes. As the U.S. Supreme Court said in the case of U.S. v. Jacobsen
“[t]his text protects two types of expectations, one involving ‘searches,’ the other ‘seizures.’ A ‘search’ occurs when an expectation of privacy that society is prepared to consider reasonable is infringed. A ‘seizure’ of property occurs where there is some meaningful interference with an individual’s possessory interests in that property.” Homeless people, living outside, are likely to have their possessions searched and seized for reasons other than crime investigations. Maybe a public maintenance worker comes across the stuff and looks through it to see if it’s garbage. Perhaps a police officer goes through it or destroys it because he thinks it might be dangerous. Possibly, the mayor’s office has ordered crews to clean-up the streets.
If the public worker did think the found stuff was garbage, the first thing a court will consider in the search and seizure case is whether the owner expected that his stuff was in a private place. Usually, when police have searched through garbage left for municipal collection at a curb, in an outside garbage can (even up against a house or in a permanent location somewhere),  or in a shared trash receptacle for a business or apartment,  the courts believe that the person who put out that garbage would not have had a reasonable expectation of privacy in it.
So, when people probably don’t expect that their things were in a private place, searching those things does not violate the Constitution. An owner must show that he did expect that those possessions were private if he is going to prove that the search and seizure were illegal. 
Even though the stuff might have been stored outside or inside a property where the owner of the stuff does not even rent space, there are ways to demonstrate an expectation of privacy. That expectation of privacy must be considered in light of what the police have to prove for their defense; in court the police perspective will be heard right alongside the perspective of the person whose things the police went through or took away.
The police have to show that what they found was equivalent to garbage. In order to successfully prove that the things found outside were like garbage, the police or other government employees have to show that they believed those things to have been unwanted like garbage. The legal term for that status is “abandoned”.  Proving that property was abandoned means showing that the owner relinquished control over it.
The owner of the possessions, trying to show that he or she did not abandon those possessions, is likely to explain the situation that led to leaving those items in that place. That explanation might say that effort was made to hide the stuff or that it was arranged to clearly serve as a sleeping area or that it was located in an area well-known to be inhabited by homeless people, etc…
If that explanation is sufficiently detailed and sensible, the court is more likely to find that the owner truly did have an expectation of privacy regarding those possessions. That court decision would mean that the search and seizure of those possessions was in violation of the federal Constitution’s Fourth Amendment or the comparable state constitutional provision. 
This may raise another question, what if some ordinary citizen who is not a police officer takes something that has been left out for garbage collection? Does that result in an illegal possession? The argument that applies to the police also applies to everyone else: anything that is put out for garbage collection is presumed to be abandoned by its previous owner.
Taking it away is not stealing it. The Model Penal Code (Section 223.5) definition of larceny relating to found items even says that the finder has to know that the item was “lost, mislaid, or mistakenly delivered” in order to be guilty of theft. Even when things have not been properly put in trash receptacles, a person who takes a found item honestly believing that it was discarded has a good argument against a theft charge. 
[i] U.S. Const. amend. IV.[ii] Id.[iii] U.S. v. Jacobsen, 466 U.S. 109, 113 (1984).
[v] U.S. v. Michaels, 726 F.2d 1307, 1312 (8th Cir. 1984).
[vi] Commonwealth v. Krisco Corp., 653 N.E. 2d 579, 582-583 (Mass. 1995).
[vii] 1 Am. Jur. 2d Abandoned, Lost, and Unclaimed Property§ 3 (2006).
[viii] Since the first ten amendments to the Constitution were written to control the behavior of the federal government, a Fourth Amendment claim cannot be used alone to charge that local, county, or state police have searched and seized illegally. It is necessary to also identify the Fourteenth Amendment which makes the provisions in the Bill of Rights applicable to state governments. The state constitutions also have search and seizure clauses enabling someone to bring the same kind of case in state court instead of federal court. The great value of bringing it in federal court is that, if necessary, it can be appealed all the way to the U.S. Supreme Court.
[ix] Courts are not all consistent about this.