Be it dying or not any business you don't start from onset is always risky to buy to start growing it yourself, especially when you are not into that line of business you would face challenges, as far as I know there are many people who had barely bought some businesses within my knowledge those business are no place to stand again because the new owner is not knowledgeable enough as the previous owner.
So I am not specifically emphasizing on a dying business, both active and running are prob to face same challenging.
They're rare and usually you'll just hear this kind of stuffs from large companies that continues to consume and absorb companies. Small business owners just have limited resources to risk in running another business and yeah you're right that it is specifically if you're not into line of business that you're running even if the business itself is profiting so much that it would just require change of owner.
It doesn't matter anyway if it is dying or still a relevant business. Even Apple just came back even if it was in the edge of bankruptcy.