As others have asked, What is the illness? Makes a difference if the person has the flu, or is being treated for cancer. But I think it's also important to start with what this person most enjoys eating. The food we eat when we're ill needs to nutritious, but it also needs to be a comfort.

Also note that some patients have restricted diets. Before and after some procedures, patients may be restricted to a clear-liquid diet. It's really amazing what you can do on a clear liquid diet! For example: tea, clear broth, chilled water, popsicle, apple juice, Jell-o, strained lemonade. More at http://www.mayoclinic.com/health/clear-liquid-diet/my00742.

That recipe SKK posted looks so good. That is the kind of stuff I crave when I'm sick, too. My go to is noodles in veggie broth simmered with carrots, celery, whole garlic cloves and onion. Then when it is done, I remove from the heat and add a whole bunch of chopped fresh watercress, half a bunch of chopped cilantro, and the juice of 2 lemons. Finished with a dash of soy sauce, sesame oil and sesame seeds. Always makes me feel better!

The name of this soup is Don't Die on me Man - and it is great!
http://www.food52.com/recipes/10514_dont_die_on_me_man_a_comforting_and_healing_spicy_soup_vegan_gluten_free

Garlic soup. I'm a big advocate for garlic (and chicken-stock) based soups when someone is sick, including myself of course. I do have some tried & true recipes if you're interested. Here's my go to sick soups:

http://www.chow.com/recipes/29153-cote-dazur-cure-all-soup (so good, add a little heat, sirachi, red pepper flakes, chili powder or hot sauce, to taste - great for clearing nasal passages)

http://www.care2.com/greenliving/healing-garlic-soup-recipe.html

http://www.epicurious.com/recipes/food/views/Roasted-Garlic-Soup-with-Parmesan-Cheese-100669

http://www.chow.com/recipes/29389-roasted-garlic-and-smoky-greens-soup

http://www.foodnetwork.com/recipes/giada-de-laurentiis/tuscan-white-bean-and-garlic-soup-recipe/index.html

bacon. pork makes everything better.

I guess it depends what kind of illness it is (since it's hard to keep pretty much anything down sometimes), but I'd stick to broth-based, mild soups if I were you. The miso soup idea is a great one, and you can throw in some soba noodles and spinach/mushrooms/kale/etc, if your friend can handle them. If it's more of a sinus-y congestion kind of illness, I usually like foods that are a little bit spicy, since that can help clear things up (at least temporarily). I had a sinus infection at the beginning of the year, and I made a spiced red lentil soup with lemon (similar to this: http://www.nytimes.com/2008/01/09/dining/091arex.html) which made me feel a lot better.

Barley soup. Barley is rich in fibre, calcium, phosphorous, iron... Some sources report that barley can increase potency and boost physical strength.

Miso soup made with a mushroom dashi.

Split pea soup. Take a bag of split peas, one onion, one stalk celery, 1 carrot, 2 garlic cloves, veggie stock, dried thyme, salt and pepper. Chop all veggies into small dice. Mince garlic. In a large pot, add one tbsp olive oil and 2 tbsp unsalted butter, neat on medium low, once the butter stops singing, add veggies, except garlic, sweat for 10 minutes, add garlic, sweat additional 1 minute. Add 1 tsp dried thyme, sweat 2 minutes, add split peas, and 5 cups veggie stock. Bring to boil, reduce to simmer, simmer for 45 minutes to one hour. Salt and pepper to taste. Serve chunky or blend for a smooth consistency. Done.