I would ask you whether or not someone who is unable to produce enough value to sustain even their own lives is entitled to the products of those who are able to sustain their own lives? Do you believe a market wage till tend to be unfairly decoupled from a workers marginal revenue product in a free market society?
If a worker accepts employment in which he does not receive a high enough wage to sustain himself, then he's an idiot. A worker should only accept employment in which he receives a high enough wage to sustain himself. If all workers do this, it creates a natural minimum wage floor.
That said, I can see how getting paid $2/hr in the US could still be sustainable if a person worked an insane number of hours. Is this acceptable? Sure. Anyone who doesn't want to work an insane number of hours is free to better themselves through education, work experience, moving up through the company, finding a new job, etc.
A lack of minimum wage would ensure increased abuse of the welfare and unemployment system. Who would work for $2/hr when they can be paid more from the government just for sitting on their couch all day? Therefore, if the minimum wage was abolished, the welfare system would have to be abolished (or restricted to serve only to those who cannot work) as well.
On the crime prevention side, I believe the government should offer unlimited jobs at below-market-value, and this would be the form of monetary compensation that would replace the welfare system. Just got laid off from a construction company? Work for the government at 75% of the market wage on a new courthouse. The factory you worked for just shut down? Ok, come work on the roadkill cleanup team for 75% of the market wage until you can find something new.
I don't like the idea of government handing out taxpayer dollars to individuals, but it is a necessary evil to prevent desperation and crime. However, if they're going to hand out money, better make sure that the individuals receiving it actually work for it!