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It's called rejuvinating a mother plant. It's very simple, leave a third of the leaves and some bud material after harvest. As everyones said, if you don't leave some buds the plant will just shrivel up and DIE.
If you try this don't expect things to happen overnight of course, the progress will be really slow at first. Nothing will appear to be happening for at least 2 weeks, maybe more. Don't get discouraged and hack it down, you'll see new white flower hairs from the old buds first. Just a few here and there, nothing big. Then new shoots will start popping out from all the old buds and leaf nodes, if it was a good solid plant at harvest then the new growth could be thick. Pinch the new shoots back after they've put out a couple leaves, forcing new double shoots. Many folks rejuvinate particular plants because of some special quality, putting the clones into flower while leaving the mother in veg to take more cuttings from.
A rejuvinated plant WILL die after some YEARS of good use, the stalks phloem eventually becoming clogged and unable to carry nutes to the crown. This is why it's important to start ANOTHER "donor" plant somewhere down the line. There's a really great thread on this forum that has all the answers you'll need for a re-veggie and also search this forum for BONSAI related threads. Much much good info there about treating a "mum"
like a bonsai plant. Pretty neat stuff.
Good luck! Give it a try!