Corporations will pay what the market will support so if people are willing to work for low wages (because they have no skills and receive government benefits) then there is no reason for a corporation to pay more.
You do realize that a corporation benefits from whatever welfare their workers are receiving from the government, by not having to pay that amount themselves to keep their own workers afloat? Do you really support having your tax dollars go to prop up corporations in this manner, while their CEOs take bonuses?
Corporations have the power and money to be able to make a difference by creating programs to train these workers with "no skills", and to pay them wages that will create demand in the economy, the one in which their workers will inevitably spend their earnings in.
For some reason, you focus on the poor individual as if they somehow hold all the power and are simply parasites, but then allow the corporations (who actually do hold the power) to take no flack for the consequences of their larger scale, parasitic behavior? There is only so much that individuals on the poor end of the spectrum can do to change their own circumstances, whereas corporations have the capability to do great things for the community, given their resources. Instead, you give these corporations some sort of merit in their decision to make it a race to the bottom?
It is not a corporation's job to provide an unskilled worker skills to do a job they are not qualified for. This kind of training is very inefficient and will likely result in the corporation never receiving a return on this investment.
Corporations do not benefit from welfare as workers often give up opportunities for advancement, more hours and better pay in order for them to stay on welfare. People believe they are entitled for something in exchange for nothing.
I think the best solution would be to shut off welfare so the lazy cannot give up the above opportunities. When this happens, maybe workers will demand to get paid higher wages