[See also: the generic monopsony case.]
In virtually all industries and locations, there are far fewer employers than there are prospective employees.
In certain circumstances, there might be a single employer where a person can plausibly get hired (at least without changing fields or moving) - e.g. the market for doctors or nurses in towns with a single hospital, the market for retail services in areas where Walmart and other big box stores have driven out small competitors.
In the graph below, you can also vary the minimum wage (w_min) and the wage in a hypothetical public job guarantee program
The graph above allows us to make the following key points:
If the labor market is more concentrated on the demand (employer) side, the price that prevails is below the efficient level. This means there are fewer jobs than in an unconcentrated efficient market. Deadweight loss stems from the fact that these workers are willing to accept a wage that is below the value they would create - however, they are not hired because the employer would also have to pay existing workers more, and the increase in payroll would exceed the increase in revenue.
The minimum wage can induce higher employment and less deadweight loss.
If the minimum wage is above the competitive level (in this case, $15.33), it would create unemployment: more people would want to work at this wage than the number of jobs. (However, the employment level may still be higher than with a very low minimum wage)
Shifting w_public to above the competitive level does not create unemployment, because the availability of a decent outside option truncates the supply curve itself.