Literally the user has no rights in that case.
What property rights do attach do is clearly peoples physical property with precedent going back thousands of years before we dreamed of copyright. By extension the files on said property ought to be secure against vandalism courtesy of more recent rules.
Believing that a running application on another persons computer transforms their physical property into your property requires magical thinking. The IP right is an orthogonal issue that has no bearing on their right to their own machine and their own files.
Its as if you stole my pen and went on to write a manuscript and I broke into your house and burned it.
Both acts are orthogonal and the ethics don't intersect in the wholly magical way you imagine. I would owe you one pen or the money to buy one and I would owe you for your manuscript plus owe the country for the crime of breaking and entry or in this case inappropriate access to a computer.
You could say they had no obligation to you since you didn't pay for the software certainly they have no obligation to run for example or not to crash or lock the user out but it seems like once you start destroying user data you are violating the users rights to their own property.