Can a aux cable be connected to a 2001 Mitsubishi eclipse on the factory stereo?

The Auxiliary input is just Line In, meaning you have a typical input going in. If you're putting a new aux input into your system, you shouldn't have an issue. If there is a tape deck, use a cassette adapter. My personal recommendation is not to get a Monster cassette adapter since there can be distortion and an issue with the stereo seperation. It's probably not standard in a 2001 model of any kind, so if you don't see it, it's probably not there. If you still want to be sure, check the owners manual.