It is totally possible because legalized theft exists in nearly every society
For nearly everything that is typically considered a crime, there is some legalized version of it that society engages in for the purpose of keeping society stable and functioning, or for some other benefit. "Murder" is the illegal version of killing people; legal versions of killing people are called "self-defense", "war", and "capital punishment." They have different moral overtones than murder, but they are all still killing people.
Theft is the illegal version of taking other people's property. There are multiple versions of legalized theft that have been in widespread practice and are still in many societies today.
If a private citizen approached you and asked you to give up a percentage of your income, or part of the value of your land, with the alternative being spending time in a dungeon, this would be called theft, and we would lament the threat of kidnapping. When the government does it, it's called taxation, and few people complain about jailing someone who skips out on paying their taxes (assuming you have a tax system which is progressive and people agree on the moral necessity of doing so.)
If I take your land away to do whatever I want with it and pay you whatever I think it's worth, but don't give you the option to say no, that would be called theft. When the government does it to build a highway or a military base, it's called eminent domain.
When Robin Hood steals from the rich to give to the poor, he is a thief but is considered a noble one, especially because the rich people he stole from were jerks, and the poor people were really poor and could use help.
Sometimes governments decide to play the role of Robin Hood, by seizing property or money specifically to give it to other people. The relatively benign versions of this would be welfare programs common in First World countries. The less benign versions of this existed during the establishment of communist countries, in which private property (except necessities) were taken from everyone and given to other people because private property was considered immoral.
The secret ingredient is a compelling moral justification
I don't mean for this to read like an anti-government rant. Government comes up in all of my examples about taking property because it's the one institution that is typically allowed to do things that private persons are not allowed to do because it can morally justify those actions in the name of creating order and preventing anarchy. Private people or groups can use their own moral justifications (and they do with things like killing in self-defense), but it's harder to do that with theft, especially in advanced countries that value property rights. But, that's where your own society can have different values, or different priorities on those values.
The trick I see that you could use is that your imaginary society could have rules against the actual act of stealing, but find it morally virtuous to give those stolen things to someone else. That way, if you recieved stolen property (or "recieved it") there could be a moral argument that you should be allowed to keep the stolen thing because you deserve it more than the person it was stolen from.
You can have "stability" with all of this justified theft, but at the expense of being poorer than you otherwise would be
I think it's pretty clear you can have stability and permit people to keep ill-gotten gains... but that's going to reduce the incentives for people to have things worth stealing lying around. They may invest in things to prevent thefts, or go to effort to steal their things back (what would be wrong with that in your scenario?). But, that takes time, effort, and resources, things which most people throughout history have had very little of.
So, if you're not a rich person, the rational thing to do is avoid all of that trouble by not having anything to steal in first place. This is a large part of why there's poverty in the parts of the world where property rights aren't respected; it's a lot less effort to stay poor than to be rich or even moderately well off. You should keep that In mind when designing your master thievery society; it's probably not going to have anything resembling a middle class, because common people need to be able to keep their valuable things in order to have a middle class.