OK, well, by that definition it's not fraud, then. If I lie to you to convince you to not cancel a service you're already paying for then I'm not depriving you of anything. You're willingly continuing to trade your property for a service. For it to be fraud I would have to trick you into giving me something for nothing.
I don't understand your logic, and your statement isn't true.
Fraud doesn’t require someone to be "tricked into giving something for nothing." Courts have long recognized that it’s also fraud when one party induces another to act (or refrain from acting) by relying on false or concealed information.
That’s why there’s piles of case law on fraudulent inducement (getting someone to stay in a contract by making untrue statements) and fraudulent concealment (hiding negative information so they remain in the relationship). In both situations, the injured party continues performing under the contract to their detriment because of deception.
The key element is reliance on a misrepresentation.