Exmaxima has it right. Insulation decays over time, and metal case tools can become live. If you have access to a ‘megger’ (might be a British term) you can easily test the insulation, but I don’t think there’s much doubt!
Here in the U.K. where we have 240 volts, you wouldn’t use anything without an earth, and most of our circuits are protected by ‘earth leakage’ breakers as well. However, we still get the same problem of insulation breaking down, it just causes the breaker to trip.
If it’s a decent quality motor, such as a British made machine motor, I can get them rewound locally, which resolves the issue.
If it’s a power tool, it’s probably not worth it. And while I know newer isn’t always better, in the case of power tools it often is. I had the same problem with an old power drill of my Dad’s. I thought about having it repaired, mostly for sentimental reasons, but the Bosch drill I replaced it with was about 2 generations newer, had a better chuck, superb speed control, and didn’t cost much more than the repair!