Brief Answer:
I am unclear where there is a question.

Detailed Answer:
but looking at the other questions, there is caring concern about what is going on with the sibling's health and if something could be done further to help a bad situation.
First, the liver does a lot of functions, some are obvious some not so much. There is immune functions the liver does. It filters the blood of plain crap and also breaks down particular toxins. It puts out proteins that help clotting AND these same proteins signal there is an inflammatory condition that needs attention and healing. A liver that is not fully functioning predisposes to more severe infections and impedes healing.
Then there are the effects on the toe. If there is edema (which there always is if there is liver failure) the fluid also goes to the feet. This tends to split the skin open and leads to infection, but also crowds out the ability of new blood to get in. Nutrients, immune cells, heck, OXYGEN will have difficulty getting down into the tow if there is liver failure.

so, while diabetes is the usual condition associated with a non-healing foot/toe ulcer there can be other conditions and the liver affects immune function, healing, and also circulation.

---

Brief Answer:
good question

Detailed Answer:
It's really common. I'm working on a research tool for it; you know those things you put on your finger to measure oxygen?, same thing, able to be put anywhere.

So, first, there are all the things that can make a sore. Burns, infection, chronic irritation or pressure on the area (most common cause). If the cause of the sore doesn't go away, neither will the sore.

Then there are the things that prevent healing. Malnutrition is quite common and certainly is present in anyone with liver disease because the liver mobilizes nutrition into forms the rest of the body can use, so if the liver doesn't function, nutrition cannot happen regardless of how much food is given; it never gets into the form that the body can use.
Then there is getting the nutrition to the site. chronic irritation and / or pressure prevents blood flow into the area. Poor vessels like with atherosclerosis (bad flow INTO the foot from bad arteries) or with chronic edema (bad flow out of the leg like with bad veins). Or there is bad flow from seepage into the foot (bad lymphatics).

that covers it.

---