I've not tried this, but you could cut the stem off well above the rotted section and either put it in water or well-drained moist compost to try and root it. If you try the latter, you will need to keep it covered, either in a big polythene bag or in a propagator until it roots.
I'm afraid there's no chance of rescuing the plant complete with rotted section; it does suggest that your plant was overwatered and/or cold.