While cats have a reputation for being somewhat haughty, they do often form strong relationships with the other cats that they live with and can become very sad and upset when something happens to one their friends. If one of your cats dies or runs away, your other cat (or cats) may become unsettled and exhibit changes in behaviour.
How do I know if my cat is upset?
Like people, cats can mourn in a lot of ways. They may become louder and vocalise more, as though seeking out their friend. Other times they become more sleepy and less active and go off their food for a period, as they feel sad and low. They can also become a little less outgoing and spend more time hidden from view, or, alternately, they may become clingy and want a lot more attention from their owners now, as they are not getting the usual stimulation from their missing friend.
What can I do?
You can treat your sad cat extra gently and give it some more pats and affection. If it seems a little tetchy because it doesn't have a friend to chase it around or if it is extra sleepy and hard to rouse, you can break out some new cat toys. These can often get a sad cat to get up or help give an energetic cat a way to use up its extra energy. You can also offer some extra-tasty food like cat treats to stimulate the appetite of a sad cat.
How long should it take for the mood to pass?
Generally, if you give it a few weeks, both you and your cat might start to feel a little better, although grief is often a gradual process in which the improvements will be incremental rather than dramatic. You may even start to feel like adopting a new cat friend to keep your cat company.
If you cat doesn't seem to be turning the corner and starting to get back to normal in a month or so, you should get it checked out by a vet. Vets can help to check that there are no health issues that are causing these symptoms, as your cat can easily have health issues that are not related to grief but that have similar symptoms. Vets can also prescribe light anti-depressants if your cat does seem to be struggling behaviourly and cannot naturally adjust to its new environment.