If you have two or more cats living together, they will become attached to eachother. The degree of attachment can differ, some cats just allow eachother and other cats can become very close buddies. When this buddy passes away, behavioral changes will usually occur with the remaining cat or cats.
And cats don’t just grieve eachother, the loss of a owner can be equally hard on the feline. The reaction to this loss may differ, some cats will search a while for their missing friend, others might have more permanent behavior changes.
Even though its very sad when one cat passes away, don’t just take the dying cat to the vet and never bring it back home. If you do that, the remaining cat(s) will not know what happened to their friend. They might think their feline companion will come back eventually and stay on the lookout for lenght of days.
Some animal experts suggest it is better to bring the deceased cat home for a day, so their friends can come to understand he or she passed away. They will still grieve and their behavior might aswell change, but they can accept the new situation better.
And cats do get lonely when they survive their buddies, they will miss the companionship and day-to-day happenings. But don’t be too hasty to get a new cat. Imagine if your partner died and the following week your family would force a stranger on you. Its pretty much the same for cats. They need to come to term with their grieve first and not all cats will allow a new cat to intrude in their home.
If you know your cat is sick and will come to pass, you could think about already getting a new buddie, so they other cat can get used to the new cat, and not see him/her as a threath.
All cats grieve in their own way, some might even become more playfull or want more attention. This is no indication for the amount of grieve, this might be a way for them to deal with it.