Im sure they do. Coco and Fluffy were kitty friends for 8 years and when Fluffy died Coco just layed at the end of the couch and stayed there for days. She wouldnt eat and we had to bring the food to her and even then she wouldnt eat. She only got up to go to the litter box and then she would come right back. She to had little kitty tears and it broke my heart. I think she sat on the couch cause Fluffy use to love to sit there and I was always on the couch and she wanted to be near someone. All you can do is give her extra love and if you are up to it, get an older cat that could keep her company like the others said. Im so sorry for your loss and I hope things get better soon.