Hi there,
Firstly so sorry to here you have lost a bun, I did too, 16 days ago.
With my bun that was now on his own i was watching for anything obvious like not eating, drinking or pooping, but he was ok on that front. But he just seemed as if he had lost his get up and go. He used to run around like a mad thing at breakfast time before we lost Coco, but after he would just hop over to his bowl slowly. Then he took to sleeping all day in the hutch whereas he would always snooze in the run before. When he did go in the run he mainly just sat there. It broke my heart to see him like this, and I imagined he was sad and lonely so we decided to try and find him a new friend. He perked up immediately, his new lady is in the run next to his at the moment as we have just started the bonding process. The difference even just having her next to him has been immense. He is back to his old self.
Are you thinking of a new friend for your bun? I do think they are often ready long before we are!