In my other question What is this plant on the pictures? I was asking about the identity of certain plant. The reason I was asking was that this plant has gone for the worse recently. The whole plant somehow faded and the liitle sprout seen on first picture has sagged and lost most of its leaves. Well, it went from bad to worse. The liitle sprout just toppled over with no roots left. My guess is that the roots have rotted away. My question is: Can I save that sprout and how. Would putting it in a water with a bit of liquid fertiliser help? Or is it gone. My worry is that the big plant might follow soon.
The problem is root rot due to over watering and insufficient light. Very common with these plants as indicated in my answer to your previous question.
There is the possibility of spider mites. Examine the underside of the leaves with a magnifying glass for what appears to be grains of salt. If present wipe the leaves, top and bottom, with a solution of 5 ml dish soap to 1 liter of water. Repeat three times at five to seven day intervals.
Do not put the cutting in water. Use a rooting hormone if available and pot up in a medium that keeps the roots moist, not wet. You can use peat, coconut coir, perlite or sphagnum moss. Be sure to put this in a high light area. High humidity with air movement helps.