1. slang Of a machine, near a complete breakdown or loss of functionality. In this usage, "its" is used between "on" and "last." Judging by all that noise coming from her car, I'm pretty sure it's on its last legs. The blender stopped working again today—it must be on its last legs.

2. slang Of a person, near physical collapse or death. In this usage, a pronoun for the person being discussed is used between "on" and "last." I knew I was on my last legs, so I was very relieved to see the marathon's finish line in the distance. Ed's on his last legs—you should probably try to visit him in the hospital today.