I remember hearing when I was young something about Native Americans not viewing theft as wrong unless caught. I understand that using the term Native American is extremely broad, but if you have any information on the topic or could refer me to some sources that talk about this, that would be greatly appreciated.
Indigenous peoples everywhere regard theft as wrong, if one family is pinching the food storage of another family then there's going to be a problem. But this is certainly a broad topic, as you're asking about all time periods and all regions...so in general, theft was wrong; but specifically in many cultures theft didn't exist.
In extreme generality, in indigenous societies a desperate family was able to rely on multiple overlapping sharing-groups, and often it was socially disastrous to not share with someone. Besides social pressure to help one another, individuals would've learned how to hunt, fish, trap, gather, and be self sufficient as children. This mentality creates societies full of adults who don't think of stealing to survive, why would you want to cause such a problem with a neighbor if you don't need to? And if individuals have all the knowledge to be self-sufficient and multiple social safety nets, then you simply don't see endemic poverty and theft as you do in Europe ca. 1500 at Euro-American contact. No one has excavated a tenement district of the working poor in a Mississippian walled town.
Everyone who was a part of an Anishinaabe village or community had obligations and duties to the entire community, as well as to the spirits. The commission of a crime upset the balance of obligations and duties and Anishinaabe justice existed to restore that balance. Restitution and healing were the preferred methods of dispensing justice, rather than retribution. Jails were nonexistent, although physical punishment perhaps was common, and public censure and shaming especially so.
- M. L. M. Fletcher
For some societies theft was de-facto impossible. Today, there exist egalitarian foragers in some parts of the Americas, and historically there must have been similar societies. If you lived in a society like this, it's easier to create any object you want than to steal it. For the Piraha of Brazil, people often quickly make a required item (like a basket) in the forest as they're gathering; and after using it once or a few times simply throw it away. All objects are treated like this. As Daniel Everett notes, even if they're given metal tools by Euro-American visitors...these "precious" objects eventually have been left somewhere and forgotten, or given away as a gift to another visitor to the community. Individuals simply don't hoard anything, so no one even acquires so much property as to make themselves a target. In these societies, no one goes hungry when everyone's mother gathers food, when every man's catch is divided equally. No one needs to steal to survive when society doesn't create that role: a class of subsistence farmers or working poor who live in desperation. These actions and beliefs by the Piraha are intentional, people know how to smoke and store i.e. hoard food - they could, but wouldn't want to. When Daniel Everett asked a man about storing food he responded, "I store my [food] in my brother's belly."
This combo of a pro-social ethos and the use of transient perishable material culture is not reserved for foragers. People living in farming villages could as well live in a world where thievery was near impossible.
Theft [in Haudenosaunee/Iroquois society] was comparatively rare, for land was the property of the community, surplus food was commonly shared with needier neighbors, and the long bark dwelling belonged to the maternal family, and the personal property like the tools and weapons of the men, the household goods and utensils of the women, were so easily replaced that they possessed little value. Practically the only objects open to theft were the strings of wampum beads that served both as ornaments and currency; but such was the value the community of spirit of the Iroquoians, so little did they esteem individual wealth, that a multitude of beads brought neither honor nor profit except so far as it gave the owner an opportunity to display his liberality by lavish contributions to the public coffers.
– The Indians of Canada, D. Jenness (1934), pg. 135-139, excerpted in The Iroquois: A Study in Cultural Evolution, by F. G. Speck (1945) pg. 32-33
[In Tsalagi/Cherokee society] Rather than coercion and punishment, social sanctions like ridicule, withdrawal, and ostracism, were used to bring wrongdoers and non-conformists back into harmony with the community.
Of course, theft still existed; humans aren't perfect, but when it happened the source of the problem was dealt with. The elder Isaac Chamakese speaking on the subject of Wahkohtowin (Kinship), also called Cree (Nehiyaw) Natural Law, mentions a historic example of a man who stole a horse from another. His friends heard about this and discussed what to do, they decided to force the thief to work for the victim on their farm. Once the thief actually knows the life of their victim they wouldn't think to harm them, and in remembering one's responsibilities and relationships with one's community the person rejoined society. As in Nehiyaw law, the Anishinaabe concept of Mino-Bimaadziwin "the good way of living," meant that each person was upholding their responsibilities to each other, to the earth, to the spirits, to the ancestors. So the reason behind legal action in such a system was not to punish, but to restore the criminal back into this social framework.
This concept is widespread but not universal, and "eye-for-an-eye" responses to theft also existed. In the 19th century the Umonhon (Ohama) punishment for theft was for the offender to pay back the value of the stolen property then to be flogged by "police" (select members of a warrior society tasked with enforcing law). As u/Reedstilt mentions in this post about indigenous North American legal systems in the 17th century Wendat legal system, theft was punished by restitution but also included the victims taking anything they'd like from the offender's longhouse. To quote Reedstilt,
The Wendat at this time had a very narrow definition of theft, which essentially only included items taken from a home without the owner’s permission or forcibly taken from a person. Something left outside unattended was, legally speaking, fair game. If a victim of theft recognized their belongings in the possession of another person, they had to ask the current owner where they had acquired it. Refusing to answer the question was seen as an admission of guilt. If the current owner said they had gotten the item from someone else, the victim questioned that person, and so on, until the original thief could be identified. Once the thief had been found, the victim and his relatives were allowed to go to the thief’s longhouse and take whatever they desired.