Buying and existing business is very risky and if you could have that chance and patient to nurture and start growing your personal business would be more better. Know this and have peace of mind, to every business there is a secret and if you buy a business you don't have the idea of or because you noticed there's much profits from that business and you think if you buys it you would also starts making such profits is something impossible, although sometimes it doesn't work that way.
It's risky, but why bother settle for a dying business if you can buy the one's that's still continuously relevant. OP even indicated that assuming you have the given resources available anyway so there's that. In that case, it would be riskier to start new ones. Let's say that here in my area there's that monolith Starbucks in the center of my city and many business owners would just build coffee shop around it. Surely most of them would just crumble.
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 thes 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.