Assigning ownership to money

How would a society function if money could be assigned ownership, so that no transaction could take place without the owner’s approval? I know this is a stretch given that individuals could still force an individuals approval. Thus let us assume that whatever market for theft, the costs are outrageous in comparison to the benefits, thus all rational theft stops (irrational theft would thus mean individuals who spend additional money than what they wish to collect. There is most certainly a market for embarrassment in which one might spend more to watch someone lose). Thus we have a system where theft is virtually eliminated. How would the market operate without possibility of theft? Of course theft can take place in the form of fraud. Would individual criminals shift their faculties toward deception rather than theft?

What?

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