Can you fix rubber on a handle after it has all but turned into a liquid?
I've had the same problem with other types of rubber-coated tool handles. The best solution is to completely remove the rubber coating, which takes a lot of scraping and then scrubbing (outdoors) with paint thinner on paper towels. Invariably, as you have already noticed, everything touched gets coated with hard-to-remove black goop.

Another choice would be to wipe off the loose stuff and then over-wrap the handle with a strong cloth tape, checking carefully that it will not slip when you use the maul. 

You might cover the tape with heat-shrink tubing, if you have the right diameter stuff, or with tubing cut from an old bicycle inner-tube (cheap or free, and makes a good grip).