You've got a base on it, so it might just root. It's worth trying.

If it were just leaves, I don't think it would root.

That happens sometimes with Alocasia, some type of fungus or bacteria gets in and starts the rot. The plant will keep going but usually so will the rot. Completely cut out the rotten part and plant into new soil (and new pot if you can't sterilise the old one). Although I found it didn't help with mine, the rot eventually came back, yours might be different. The only way to find out is to try. Good luck with it.

I cut off all I could and hollowed out what still looked rotten. Will plant in a new pot tomorrow. Is there anything I can put on the cut part to help it heal and grow new roots? Barbara

Cinnamon powder is usually good against fungus.

I can do that. What about rooting hormone? I just have the one you buy in stores.

rooting hormone probably wouldn't hurt, whatever you've got on hand.

Do I put it on the cut bottom part and/or the hard 'shell' outside?

Coat all the exposed parts where you made the cuts. But it wouldn't hurt to coat the rest in case there's something there as well.

Barbara, were you able to preserve bottom part? what about the top? same thing happened to my plant.

I dont know who will ever read this, but I accidentally snapped a small trunk from my elephant ear plant. I removed as much of the rotting bits from the end and said screw it, ill shove it into a small pot of fresh growth medium ~2-4 inches deep. (I only had my 50/50 soil & peatmoss mix). I left it on the patio for a couple of rainy days and BAM, it began rooting again at the base. two weeks later its grown another two leaves and a new daughter plant has sprouted next to the trunk.

when in doubt, shove it back the dirt and see what happens!