babyboots— Hi, I'm Fi ("fee"). I'm replying to your heartbreaking story even though I only just joined this forum and haven't had a chance to introduce myself. First off, I am SO sorry to hearing about your wonderful Boots. I am sure that even though you only had her a few days that she died knowing she was loved. Given the story of not eating and then liver failure, it's possible Boots ate something that poisoned her—like a plant that's poisonous to cats. Was Boots an indoor-only cat or did she go outdoors? My husband, who is a botanist, suggested that Boots might have eaten lilies. But that's just one hypothesis.
But I have a more important message: You need to be there for Carl. He's only been with you for a few days, and so is not going to feel secure yet in his new home. And now he's lost his sister. He is going to go through just as intense a grief, actually more so, than you are feeling. He needs your support and love. And most of all, he needs your protection. If he's an outdoor cat, or if you have houseplants, you need to be sure there are not any plants that are poisonous to cats that he, too, might chew on and get liver problems from. In short, you need to make sure he is safe. If he's eating fine and shows no signs of illness, then probably Boots is the only one who might have eaten something, like a plant, that poisoned her.
How do you find out what plants are poisonous to cats? I suggest you google that information.
The other reason you need to be there for Carl is that his grief alone, without any other factor, can be acutely dangerous to his health. My husband and I have, over the 40 years of our marriage, had four pairs of cats—every single pair male and female littermates. And of course, it was nearly inevitable that one of each pair died before the other. In our experience, the grief a cat feels from losing a sibling can make them sick—or at the very least, be such a severe stress as to cause depression and immune system impairment.
Your experience of seeing that tuxedo cat near Boots as Boots was dying suggests that Carl was with her on some other plane, and knew she needed his support. I don't mean to sound nutty: such things do happen. I have seen a similar event myself.
So Carl knows that Boots has passed on. He needs you to be strong, and to take good care of him.