Yes you can, first let the plant dry some. what has happened is the stolen has rotted off. I used to just toss those plants, but I was sent a really nice Neo pup that I really didn't want to lose so I put it so just the end of the plant was in potting soil, but it took months to root, and I had to be real careful with moisture so it didn't begin to rot again.

A short time ago Bob started a post about rooting pups in water. I had just found a pup of Neo. compacta "dwarf form" that had the stolon rot off. I went to the second hand store and purchased a bud vase for 10 cents that looked like it was the right size to hold the pup so just the very end was in the water. I change the water every few days, after only about a week I already have roots.

Here's a pic......

{{gwi:510355}}

Phee78,
You should give a try to what John suggested above and hope for the best. From the looks of your plant,and the rank odor you mentioned,I'm skepticle of survival tho.
But sometimes broms can amaze us with their come-backs,and I'm hoping yours will do that for you.
You might also try dipping the dried out base in rooting compound too,as it may help to contain the spread of whatever caused the rot to take hold.
Bob

Phee, it's a bit hard to see in your picture, but it looks like there is a brown zone at the base of the leaves. If this feels mushy all the way through, then your plant is a goner. If there's still some firm tissue there, clean it off as best you can and try rooting it. I haven't tried Bob's water method but I find that sticking the cut end in some pure perlite and keeping it evenly moist works about the best for me.

Phee, I agree with Lisa that damp perlite is a very good rooting method,and is used near exclusively at our Botanical Gdn. There is a 10x4 ft.table section filled with perlite where all types of plant rooting takes place,and I'm really surprised how quickly roots develope. With strong light/sun,70-80deg.warmth,and programed misting,most any plant there develops a good root system in a week or two. I don't know why perlite works so well,but it does. I've tried it at home too,putting an offset in a shot glass (or similar) filled with perlite,and half filled with water.This method works well too,but its important not to let the perlite dry out,and daily check-ups are needed to keep it moist.
Bob

The base isn't mushy at all. All the leaves are still firm, even the purple-ish bits further up.

It seems to have dried out and doesn't smell anymore, so I'll try and get some roots happening and keep my fingers crossed.

Thanks for the tips, everyone! :)