Hi Tagon,
My condolences for your loss.
Dogs can actually go through a type of "grieving" for a lost member of the pack... There are quite a few theories out there as to exactly why. I lean towards the idea that the pack order has been disrupted, the dogs know there is someone missing, and they're waiting or attempting to get used to the new situation. This is especially so when it's a matriarch or dominant individual. There's other reasons out there, but this fits my view best

Going off the feed is not an uncommon symptom of this. Usually it takes about a week or two for everyone else to get back to normal. That said, your non-eating dog is 11 years old... geriatric for med-large breed and could be that for a toy-small, depending on his/her physical/mental condition. If there's some leeway for weight that can be lost (dog is pudgy), then just wait and be patient. But if needed weight is being lost and if there's no improvement over a day or two, take him/her in to the vet for a physical checkup. It could be more than just readjusting to a "lost" friend.
all my best,
toodles