When we lost our second last hound, the one left, her brother, was really upset although I suspect as much to do with being the only hound after never being in that situation, from birth, as missing her. It hit me badly too. She'd been very ill (cancer) for some months before we had to let her go. So it wasn't as if they'd had much interaction for some time. She was just there and then not.
However, much as we started taking him everywhere with us rather than leaving him home alone (and if he couldn't come, we didn't go), we tried to keep to his normal routine as much as possible, and didn't 'baby him' because all too often that can reinforce the feeling that there is something to be upset about.
Our previous losses was clearly accepted by them as part of life's cycle. Comings and goings and none of them really reacted.
Eventually that last boy adapted and by the 4 months it took for a new buddie to join us, he'd actually settled down, although he'd still react badly if another strange dog as much as looked at him - he'd lost his pack backup!! I don't think he was especially keen on a 9 week old WHIPPET!!
If you are fostering this dog, can the people who you are fostering for help?