That's normally true, but only if keeping someone employed under higher wages is still net profitable. Otherwise, an employee will be layed off anyway.
When current wages prevent full employment (sticky wages) or lead to cost-push inflation (wage-price spiral) wages are too high.
Companies aren't charities. They do what should do: Make profit. If you want to prevent this, use government regulation to make this unprofitable. Preventing companies from making profit will never work anyway.
Generally speaking, when companies make loss, it is an indication that the unprofitable action in question is wasteful. Government spending and regulation may be used to rectify it, but if it is inpractical or doesn't pay for itself, then it's obvious that it is a wrong thing to do anyway.
And who'll pay for this? No one ofcourse! Rising minimum wages generally (though not always) backfires because too many employees will become a net-loss for a company, and hence will be laid off. Perhaps a taxpayer funded negative tax bracket for low income workers may have the effect you desire. It'll increase low income workers incomes without comprising their employability.
How'd you explain the 9% unemployment, mainly among low-income groups? The market clearing wage is much lower than the average wages currently paid, mostly because the economy still suffers because of the effects of sticky wages. That's why the Fed carried out QE.
