Is it possible to soak the container in water, to soften the lower part inside, so you can gently tug the plant out. Then let the plant air dry thoroughly, so the roots that may have gotten injured as you pull it out can dry out and heal properly.
Remove all the dried out leaves, clean it up. At this time of the year my desert rose is just dormant, either with leaf or no leaf. So I just let it be, no watering, no fertilizing till it wakes up again in mid Spring, where I can resume all the fertilizing or repotting as needed.