What is the origin of the idiom, "On his last legs?"?

Have you ever noticed cows and sheep, after they have grazed, will sit, both sets of the lower part of their legs curled under them. Then, of course, they stand up and graze some more.

The origin of the idiom is from the care of domesticated animals, who, near the end of their lives, can't stand up on their legs anymore. Hence, the idea of the animal standing, but so close to death that the next time it sits, it want be getting up again.

If it looks like the animal is so near the end this could be last time it stands = on its last legs.

The term is a contraction of "on the last power of his legs", implying that he can't go on much longer. This has evolved into an implication that a person is dying.

To be "on your last leg" is to be near the end; near collapse. You have scarce resources left to complete something. "Our old family dog is on her last leg (meaning tired, near death). The "leg" here can be interpreted in two ways. First, comparing a leg to the tired or injured legs of a person or an animal after extended effort; there is not much left to stand on. A "leg" is also a counting word for a segment of a long journey. "I would be glad to sell you my car, but I must tell you that it is on its last leg."

on your last legs | on its last legs informal

Meaning: If you say you're on your last legs, it can mean you're close to exhaustion, or it can mean you're close to death. If a thing is on its last legs, it's close to breaking or wearing out.

Hope that's helps