meaning - "I live on beans and rice" vs. "I live off beans and rice"


I wanted to refocus a related question on ell.se. towards a possible deeper and direct relationship to "on vs. off".


Consider the following two phrases:



In addition to the subtle difference in meaning, I'm particularly interested in where the semantics of the differences might come from. Can we trace the semantic difference between "live on" and "live off" to a fundamental, "definitional" aspect of "on vs. off"?




Below, I've answered my own question as an afterthought. It was additional thoughts that needed to be moved to an answer, and is in no way intended to be definitive.




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