It is possible to work and do pretty much any job when your hepatic encephalopathy is being treated and controlled by medication. It is all going to depend on the severity of your symptoms and what your Doctor advises. A job where you are alone all the time might not be the best because others can point out when you aren't acting right and you can try to fix it. Alone, you may miss the signs and end up in trouble.
Some people with HE are told that they should not drive, driving when your toxins are high and you are having symptoms is the equivalent of driving drunk.
I believe that when your HE gets to the point that you aren't able to recognize or self treat the symptoms, it probably isn't safe to work in any field any longer.