Hello~I am so sorry that you grandfather is having these issues.
I would definitely try the Milk Thistle, I would use the tincture instead of capsules as it gets into the system faster. Other herbs to try are: turmeric, dandelion root, resveratrol, and green tea.
If there is a naturopathic physician in your area, I would also see him/her, they have other ideas as well such as a liver detox program which helps lots of folks.
I'm sorry to hear about your grandfather. It does not sound like milk thistle would be harmful, but it might not do much good either. If your grandfather had hepatitis C, the literature suggests it won't help. If the issue is jaundice, cirrhosis, liver cancer, or fatty liver disease, it might help to ease inflammation and maybe even promote some cell repair. In neither case would it hurt him, but again, using a botanical when someone is diagnosed with acute liver failure is a pretty unlikely way to impact it very much. Is he on the list for a possible liver transplant?