Q: The part of my frame where the sway bar attaches rusted off and is now hanging freely.

If you drive locally at low speeds, and the car is controllable, it is probably OK to use on a short term basis. I’d be reluctant to more specifically state that it is "safe to drive" though for two reasons: 1) Any vehicle that is missing basic structural or functional components can’t be termed "safe"; and 2) I would need to know more about the extent of the rust and whether that itself raises issues and/or implicates additional components. Depending on the overall condition of the frame, and the frame in that particular spot, sometimes repairs can be made which in your case might consist of a welded on mounting boss to re-establish the sway bar to frame attachment. If you would like to know whether the frame, or suspension components, are compromised elsewhere, and whether a repair is possible thus giving you some additional service life out of the vehicle, please request a vehicle inspection. If you request that service, the responding certified mechanic will inspect the vehicle and advise you right at your location. If you have further questions or concerns, do not hesitate to re-contact YourMechanic because we want you to make the most of your repair dollars and help you to get the best possible results.