To your analogy, it's more like selling a horse to the petting zoo for kiddie rides because it no longer has enough stamina for long hard rides in the mountains. It's a good deal for the seller, the buyer, and the horse.
Acquiring a business is generally only done when the expectation of future revenues is greater than the purchase price, but if the business is dying, the key is to maximize the revenue out of it so as to prolong the inevitable, and squeeze as much money out of it as they can.
Not all businesses will have a way of replacing a user base that is dropping off that isn't lower ROI than putting the money elsewhere.
If that's the case, then you extract the revenue that's left, but you don't reinvest much of that revenue - you might keep the horse while it's still doing useful work, but you're not building a new stable or hiring new stable boy in expectation of growth.