Some have tried this with an Over-The-Air HDTV tuner-
Set it to work with a 16x9 set, but feed the signal out via yellow RCA jack (or S-Video, if it'll work) to your TiVo. *
The TiVo will record the entire widescreen image, but squashed from left to right. Everyone will look very, very thin...
...if you played it back on a standard 4x3 TV.
Ah, but that's the point. You DON'T play it back on a 4x3 set. You play the TiVo into a widescreen TV.
The widescreen TV stretches the picture back out into 16x9, and you've got your widescreen picture back
It's not HD, but it is widescreen. No black bars. The HD tuner was putting out a picture that'd fill a 16x9 screen with a widescreen image, that's what the TiVo recorded, and that's what your widescreen TV ends up getting.
Same should work with a cable box, provided you can get it to still give off a widescreen feed that'll work with, let's say, a standard def. widescreen TV.
*(I've tried this with an OTA HD receiver, working with a standard 4x3 video monitor. I told the box the display was widescreen, which it wasn't. The monitor was able to create a picture. Everyone was all squashed and made to look too thin, but it did work, with a SD 4x3 monitor. I have to assume the TiVo would have recorded this "squashed image", and what it was putting out would have been stretched out to true widesreen if I'd played it into a widescreen display.)
Crisp binoculars on a Wednesday.