@Cherieconne 
to the adenium forum! I'm sorry
that your 4 year old desert rose rotted. I've never had luck regrowing the roots but you might need to save them and especially the cuttings to see if they survive until early spring and you can try to see if you can use them for grafting. However, do not toss the healthy cuttings they will survive if they are healthy and will develop fat roots over time that will resemble "caudex". See the thread for growing desert roses from cuttings.
For the last 2 photos, the caudex May have the chance to survive. If the rot is in the middle it is hit or miss wether the rot would spread or not but I always give it a chance. I dug up 3 of my big ones that have rotted just during the 4 days of wet and cold!
Best thing you could do is put some cinnamon in the middle part. Leave the caudex to dry and do not attempt to replant until the "rot" is totally healed. If there are healthy tissue left, the rot damage would heal and the caudex will survive. If the rot has spread, the caudex will shrivel and it will not survive. This time of year, let the "caudex" get direct morning sun to speed up the healing/drying. Then in spring, you can try to "water root" the caudex to coax it to develop roots.
