The correct answer totally depends upon the specific lens and also upon the manner in which you desire to use it.

Even when using a lens on a tripod, some lenses require you to turn IS off, some do it automatically for you, and others actually have IS modes specifically created for tripod use. The last category includes Canon's Super Telephoto series that are tuned to reduce the effects of mirror slap when mounted on a tripod.

Most of the problems with "feedback" that actually made lenses less stable by sensing the vibration of the IS motor and trying to correct it (which created more vibration that it tried to correct (which created more vibration...(etc.))) were with a handful of the very early first generation stabilized lenses produced almost two decades ago. But since one did actually need to turn IS off with those lenses to get best performance, there are still many photographers around today who preach a gospel that says, "IS must always be turned off when a camera and lens are mounted on a tripod." This is simply not true for most current lenses.

Whether to use IS when the lens is attached to a monopod comes down to usage: If you're using shutter speeds slow enough to induce blur from camera movement then by all means turn it on and see what happens. As with many shooting techniques, this should probably be experimented with before a shoot that has to be done right the first time!

I tend to leave IS off when shooting from a monopod as long as the shutter speeds I'm using are at least twice the focal length with crop factor included in the calculation. If I'm using a Canon APS-C body with 1.6x crop factor and a 200mm lens, as long as my shutter speeds are above 1/640 I turn IS completely off. Normally in such a case I'm shooting a sporting event that can last for hundreds or even thousands of shots over several hours and there's no need to waste battery power running the IS when it is not needed. If I'm panning while shooting bursts the IS can sometimes fight the smooth movement of the lens. If the shutter speeds are lower than that, I usually turn IS on in Mode 2 (which is panning mode for my longer lenses with which I shoot using a monopod).