My dogs ran away six days ago (June 1, 2021), and just came back today. They are skinny after being without food for probably a good portion of that time. I have heard that after humans haven't eaten for a while, if they eat a lot they will get sick. I was wondering if a similar thing is true for dogs and what precautions I should take?
Yes, you must start carefully feeding them again.
They will probably eat as fast as they can, leading to choking hazards and upset stomachs. Give them half their usual portion, but split it into 10 smaller portions. Feed one portion 30 - 60 minutes after the previous one is eaten. That means that you'll spread the feeding out over the entire day.
Do not feed anything but dog food. Any well-meant scraps from the table or even freshly cooked meals can cause an imbalance of nutrients. Dog food is formulated with the perfect balance of minerals, vitamins and essential nutrients. If you want to do good by your dogs, switch to a high-quality dog food with a high amount of meat and a low amount of grains and potatoes.
Do not feed more than half of their usual portion! And strictly avoid fatty and oily food. Since the metabolism is out of balance after a period of starvation, too much food can make them very ill and can even prove fatal in extreme cases.
PetMD writes about feeding starving dogs:
The most serious effect associated with reintroducing food to starving dogs goes by the name “refeeding syndrome.” It is well-recognized in people, but less research has been done in dogs. My somewhat limited understanding of refeeding syndrome is that in an attempt to survive starvation, the body’s metabolic pathways undergo some pretty profound shifts. When the body is suddenly “inundated” with food, these new pathways cannot handle the situation, which results in fluid, electrolyte, and vitamin imbalances that have adverse effects on many different organs, including the heart and brain. In extreme cases, organ dysfunction can become severe enough that the dog dies.
If one or both of them vomit, get diarrhea or lose their appetite, cut back to only 1/3rd of their usual portion a day for a few days until the symptoms improve.
If they handle half of their usual portion for 2 days without vomiting or diarrhea, you can start feeding only 5 times a day. If they handle that well, increase to 3/4th of their usual portion the next day and then their full portion 2 days later.
If you usually feed dry food, soak it in water to make it easier to swallow and easier on the stomach.
They might start fighting for food or one might steal the food of the other. Feed them separately to avoid over- / underfeeding.
If they have lost a lot of weight, you can switch to puppy food for a while. It contains more calories than adult food and should get them back to their healthy weight.