This isn't quite the same situation as the question asked here: How can I introduce a cat into a household with dogs?
It's also not something that's happened to me. And - fair warning - this did not end well.
People I know found an abandoned kitten that was just barely old enough to be away from its mother. They have two large dogs. One of the dogs is very playful and does not understand "small and fragile".
They were keeping the kitten separated from the dogs to prevent accidents, but the kitten got out of the room when the dogs were around, and the playful dog accidentally killed the kitten (they had to supervise this dog closely when their child was a baby - the dog despite training has never managed to understand that it can break something small and delicate). They're devastated.
How could this tragedy have been prevented?