Rescuer here with years of experience with truly emaciated dogs and anorexic, sick ones.
I agree about going slowly with weight gain -- in severely emaciated dogs, by going too fast, you can actually trigger something called "re-feeding syndrome" resulting in organ shut down (and death). We do vet-supervised weight gain with weekly weigh-ins when we're recovering a dog in that condition. She has us feed them at least 4 times a day, with small meals.
The food we usually use to promote weight gain is Diamond Naturals Extreme Athlete because it's very high calorie, and easily digested (470 kcal/cup). We've had better results with it than with puppy food (which is the other option many people use). It seems to be very well tolerated -- it gives us firm poop more readily than even vet RX food for sensitive tummies.
SATIN BALL WARNING: do not put the oil in the satin balls that many of the online recipes call for!
In some dogs, it can cause pancreatitis and major vet issues. There's no way of predicting which one will get sick -- and it can be VERY sick. Moreover, most vegetable oil is nasty stuff that isn't good for dogs. You may have a dog that can tolerate it, or you may not -- but you can't know that in advance, so it's just not worth the risk.
Instead, just buy 70% ground beef. After baking the satin balls and pouring off excess fat in the roasting pan, there's still plenty of fat left, in a natural form that the dog will be able to digest.
I do use my own version of satin balls to stimulate appetite in anorexic dogs. If you warm them up, the steam will stimulate appetite (esp. if you use a little organ meat in them). I used this recipe as a basic guide in rescue for years (omitting the oil, and usually just using lots of organic oats in place of the junky, processed cereal with all its synthetic vitamins):
Dog Treat Recipes ? GPA ? Louisville
The version I make is high-quality ground beef, 10% ground organ mix (like liver and kidney), farmer's market "yard" eggs (with shells ground up and added), *organic* rolled oats, molasses, and sometimes wheat germ. The gelatin is optional. The eggs and oats will hold them together. I bake them in a roasting pan at 400 until medium-rare because most of my fosters are immune-compromised and can't do raw.
I really want to stress that good quality ingredients matter. If you haven't been following the Environmental Working Group's testing of oats, read up on it -- they found Roundup in common, conventional brands of oats like Quaker. Roundup appears to be harmful to good gut bacteria, so you really don't want to feed it to a dog that's emaciated as they need to be replenishing their gut flora instead. I think farmer's market "yard eggs" from free-foraging chickens make a difference too, as they're full of lots of good stuff when the chickens are allowed to forage naturally for bugs, worms, and sprouts vs. getting industrial feed.
I would also have any dog recovering from starvation on a probiotic and and a bovine colostrum supplement certified as "6 hour" colostrum. There's some early research in dogs showing the two together are better than one or the other by itself. This is the colostrum that I use: