Lincoln, thanks for your question. I don't know that I completely understand what you're asking--but I'm going to answer what I think you're asking.
If the cat was a completely indoor cat, the chances of her actually leaving the house to die is very, very small. If she was an indoor/outdoor cat, she may well have been injured or lost. It sounds like what you're describing is a cat that absolutely never, ever leaves the house and usually stays in your sister's room. If this is the case, checking everywhere is the best thing to do. Closets, beneath the bed, behind the bed, all furniture, inside of the pantry, washer/dryer, etc. Sometimes cats get locked in the strangest of places. If there is a chance that she's gotten outside, you're right in checking everywhere that you can outside. Calling the local ASPCA and Animal Welfare groups to help locate the cat if its brought in as injured or lost would be another thing to do.
To completely answer your question outright of whether or not a cat will leave home to die, the answer is it really depends on the cat. Some cats absolutely attach themselves to their owners and stay close to their owner around their death. Some cats seek seclusion when they dont feel good and prefer not to be around humans at that time as well--those would be the cats that "seek other places when near death".
I hope that I've answered your question correctly. If not, please click reply so that I can help you further as I may have not understood the question correctly. If my answer has helped, please click accept. I personally don't get paid for my hard work unless you click accept. Thanks so much and good luck!