I'm 80% sure that's not how violins work
Actually, that is how they work, assuming the broken string doesn't interfere with the others. The E string is the highest pitched one, so you can achieve all the same notes by just moving your fingers further down the next string over. It's just more difficult to do that, since the spacing between the notes is more precise and closer together.
Another instrument called the viola actually does this fairly often, since it's highest pitch string is the same as the violin's second highest, and even has a wider range due to also having it's 4th string be lower pitched.