When you pulled it out of the soil and stuck it in water, did you recut the end? If not then I would do that first. Keep the cut semi-close to a node as this is where the roots will come out. Use clean water so that you can keep germs down while it is rooting.

I would not callous the ends of this type of begonia (only if it is very succulent in nature). How long ago did you cut it? Was it already wilted before cutting? Hopefully the cane/stem is still viable for rooting.

The leaves should perk up within a few hours of putting it in water unless the cane was already collapsed. Also cut off the bottom leaves leaving the top 2 - 3 leaves. If the leaves are large then you can cut those in half as well.

Do pay attention to the water turning sour. I would change it out before it starts to smell (read every couple of days until it roots). You can put a baggie over it to raise humidity and keep germs out of the water too so you won't have to change water.

I didn't cut it before planting the first time, as it already had a small root system. This was a shoot we pulled out, but didn't soca food job with its roots. I cut it again last night, the cane is kind of soft and a little concave, likely the collapse you mentioned? I will go put a baggy over it. Think there is any hope? If not, any pointers how to avoid this in the future?

If there is rot in the stem, continue going up the stem to the next node and cut below it. If it is rotted out continue to the next node. Hopefully there will be some healthy tissue left. PS - you will need a node or two for cane cuttings. See Brad Thompson's excellent guide on propagating begonias (canes in particular).

http://www.bradsbegoniaworld.com/prop.htm

In the future, cut healthy stems/canes and put in good potting mix or water ASAP. If you can't do it right away, put the cutting in a baggie with a damp (not wet) paper towel wrapped around the cut end. The paper towel is a little extra insurance but isn't really needed if you pot up in a day or two.