According to that argument, if your current salary is zero, a single cent would be adequate to get you to do anything.
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Yes, if that's the best alternative. In practice no, because there are better alternatives (i.e. being a Wifi hotspot for 20$/day).
If interpreted broadly (any source of financial support), zero salary means I am literally starving to death soon. I'd do a lot of things before letting myself die. But in practice, the opportunity cost of doing your 1 cent job is just too high, even for desperate people.
You would still die, just after being humiliated and while clutching a penny. It would be a bad decision to do anything for a penny when you were making nothing, and the person who got you do do it would be a bad person. So, as a society, we choose an amount (not a factor of previous earnings) that is minimally acceptable to us, and if that wage is too high to be profitable for anyone, we prefer (and I prefer) that we just help and not profit. That's a social safety net.
Basically you've already conceded that, we're just discussing the amount (to paraphrase something else). I feel it's already been adequately set by law.
Obviously homeless people will disagree with you since they cannot find a job at minimum wage and help is just not coming to them.