
With mine, when we had our small pack, the comings and goings were really seemingly taken without much reaction. When we lost Harmony (Minnie) nobody would lie in her place by the fire for quite some months until eventually they did but that was about all.
The biggest and understandable reaction we had was with Mannie when we had to let his sister Elsa go. Not only was he obviously very reliant on her being there to ward off 'trouble', he'd never lived as an only hound until her loss so it was to be expected. I always 'hoped' he'd go before her, anticipating this because of the nature of the two, but it wasn't to be. I knew we had to find another companion but it took 4 months before Teazel arrived, by which time he'd actually settled into his solo existence, and for sure, we took him everywhere with us. If he couldn't come, we didn't go, or only one of us went so somebody was with him pretty much 24/7. I'm not sure he enjoyed his life after Elsa (I know I didn't) but he tolerated it. I don't think he especially liked Teazel and certainly would head for his chair when she had the zoomies. She didn't miss him when we had to let him go (oral cancer) either.
After Frankie had come and gone, Teazel seemed ok but again we made sure she wasn't left alone very often.
Then came Mo and Teazel accepted him much as she was very vocal when he first arrived. After Teazel went, I watched Mo carefully to make sure he was going to be ok on his own (getting another wasn't really on the agenda). He'd come from a kennel set-up with a load of companions. Thankfully he's been fine as the only hound with us so no sign of him being lost on his own. He can be 'clingy' but that's all.
I think it depends a lot on the vibes coming from the owners plus how close the relationship was between the one that dies, and the one left.