Most states have laws that dictate the reporting of serious crimes like felonies. I would refer you to the law in your jurisdiction. That being said, in your scenario a business or business owner has caught someone stealing. In theory, could the business owner or manager either take the merchandise or money back from the employee and not report it to the appropriate authorities? Yes, they could but I am not sure why they would want to. Even if the owner or manager did this, it still might be illegal depending on the state in which this act occurred. Theft is a large problem in most retail outlets.
If you are talking "caught in the act" or such, sure, an employer can take back what is thiers as they are the "rightful owner".
While, at least in my state, a person has a duty to report a felony, if the crime is upon the person themselves, there is no affirmitive duty to report such.
Be advised though, if a company makes an error and takes the person's money when they did not commit the crime and prove it later, the company faces legal consequences.