> This is never true and just economic denialism. There is a market price for labor. If there is no supply at a given price it is not evidence that a market does not exist, only that the demand is mispriced.
There can be situations where the market for a particular type of labor does not exist. Populations aren't infinite, and if there are enough good paying, desirable jobs for full employment, then there may be no one available to do a job economically.
For example let's imagine a hypothetical town where only residents of the town are allowed to work in the town, though they can provide services to those outside of the town. Let's say 100 people live in this town, and they are all doctors. There is a hospital in this town that needs 100 doctors to run. There are other jobs to be done in this town - someone needs to pick up trash, someone needs to mow lawns, someone needs to sell food, etc. Now if you pay someone a doctor's salary to pick up trash, they could potentially leave the hospital to do that job instead; but then the hospital is understaffed. Something isn't going to get done; indeed in this scenario where there are a lot more jobs to be done than people to do them, a lot of stuff isn't going to get done, no matter how good the pay is, and the jobs that are done will be insanely expensive.
In this case you would simply allow people from outside the town to work in the town, or get more people to move into town. If you scale up this scenario to cities, provinces, and ultimately nations, it's clear that at some point you must choose between structural unemployment (ie number of workers greater than number of jobs to be done), bullshit jobs (people who would be structurally unemployed are hired to do unnecessary tasks), a managed economy (employment opportunities restricted to ensure necessary work gets done at any population level), or immigration/emigration of labor (labor supply varies to meet demand) regardless of wages. In practice you'll likely get a combination of the above.