They don't seem to care that their dogs are dead because they never come looking for them.
I have only had one experience with this but it was fairly enlightening so I'm gonna share it. I saw a human shaped figure a few tiles away from my homestead on the wilderness map, so I figured I'd go investigate and see if if was someone who needed their ass kicked (a robber). It was just Olli, a fellow Kaumo hunter, and his dog. I left Olli and his dog to their own devices and returned to my homestead. That night, I awoke to "strange noises", and discovered that a dog had found its way into my medium deadfall trap that I keep baited right outside my cabin and got itself a little banged up. Assuming it belonged to Olli, I released it and went back to bed. The same exact thing happened the next night, and again I released the dog and went back to bed. After getting woken up for the third night in a row, I realized the dog didn't really want to live after all, as it had gotten itself injured three times in a row in the same trap over the same piece of spoiled meat. I decided that my fine battleaxe would be a more humane end to his suffering than his chosen method of repeated blunt injury, and I also needed a set of dog fur mittens as they help when fighting bears, so it was a win/win really.
A few days later I left on a trip to another region to look for some seeds to help expand my farm. When I returned two weeks later, a swarm of foreign traders had descended on my homestead. They had nothing I was interested in purchasing, yet they insisted on hanging out for a few days and taking a good look around my place, taking special interest in my sauna which I was able to determine by hearing the door open and close about a hundred times over those few days. During one of these evenings I was attempting to get some blacksmithing done amid the clamor of nonstop sauna door action when outside my window appeared a lone Kaumo hunter. It was Olli, and Olli was pissed.
Being severely fatigued due to my smithing I was in no shape to fight, so I pulled out my axe and shield and backed into a corner, waiting for Olli to walk around to the front of the house and come in through the front door. Instead, I heard sounds of fighting to the West. Assuming Olli was out for blood and picked a fight with the first humans he laid eyes on, I thanked the gods for the chance to rest my fatigue away. By the time I had finished resting, the sounds of fighting had quieted down. It was pitch black outside, so rather than wandering around in the dark and feeling somewhat safe due to the sudden lack of activity, I went to bed, determined to scout around the next day and see if I could find Olli's body. I was awoken by an uninjured Olli planting his axe in my hip. Unable to stand, I managed to get a good enough swing at him from my bed to knock him on the ground, and then to finish him off with a solid hit to the neck. Thoroughly confused by the situation, I crawled my crippled ass all around my cabin to the west where I had heard sounds of fighting, but never found a trace of the foreign traders. Months later in the same save, I still have no idea what went down that night, but it damn sure made a hilarious memory.