You may see your cat as the epitome of composure, but that doesn't mean that she isn't susceptible to intense feelings of emotion, whether pleasant or unpleasant. When a cat has spent her entire life with a littermate, the bond is often tight-knit, strong and virtually impossible to break.
Kittens typically form intense bonds with their littermates. Practically right out of the womb, kittens start rough playing with each other, sleeping on each other and even grooming each other. The early interaction with littermates is key for cats. It serves as a stepping stone for social development in felines, from learning how to restrain biting to pure comfort seeking.
If a cat continues to live into adulthood with her sibling, the bond will probably only strengthen. Because of this, you may notice that many adoption centers prefer adopting out siblings in pairs. Cats do well with routine. If a cat is comfortable with and used to the presence of a sibling, then that will become her routine and she'll be content with it.
Cats who live together in the same household often develop strong connections. When no humans are around, they are usually together to play. They enjoy treats and mealtime together. It's not difficult to imagine why a kitty would have a major bond with a sibling.
As mentioned before, cats thrive on routine and generally abhor change. When a feline loses a sibling that she lives with, it may change her everyday life drastically. She might not have anyone to snuggle up with on the sofa while all of the people in the household are away at work. She may have no one to chase after the laser ball toy with her.
Cats are intuitive and know when things have changed. If a cat is grieving her lost sibling, it will probably be obvious. She may start frantically looking everywhere to find her absent companion. She may completely abandon her meals and treats. She may go into hiding or start sleeping a lot more. Interest in self-grooming might go straight out the door. You also may have difficulties sleeping at night because of your lonely kitty's nonstop meowing and yowling sounds -- aww. In many ways, the feline grieving process isn't too different to that of a human, strangely enough.
No set time frame exists for determining when a cat is going to just "bounce back" after such a big loss. Like people, cats can't just recover from grief on a dime. The process could take days, weeks, months or perhaps even years. The only thing you can do is try to make things a little easier on your precious pet. Give her plenty of love and attention. Play with her every day. Cuddle with her. Remind her that you care about her, as alone as she may feel at the time. She deserves it, after all.
Allow your pet time to recover and heal. If you feel that your pet may benefit from some help, set up an appointment with a veterinarian. She can talk to you about kitty anxiety-easing medications.