> I see what you mean, but do they really?
Yes, they really do. E.g. if the company was dissolving went into bankruptcy proceedings the employees would have a claim.
> If I leave work one day (say, in the middle of the week) and don’t come back, does my employer owe me pay until the day I left?
In my jurisdiction we have at-will employment and it works both ways - either party can terminate the arrangement at any time. In practice, employees usually give notice so as not to poison relationships.
On what basis would an employer not owe an employee for work performed?
> the employer does not owe the employee anything until the pay is actually due, as specified in the contract.
You have confused owing a debt and a payment schedule for the debt. When you take a mortgage on a house you owe the bank money (probably a lot of money). The fact that a payment schedule exists doesn't change the the status of the status of the debt nor does it prevent the bank from paying interest.
Second, you are assuming there is contract - in my experience most workers are not operating under a contract.
Of course, I'm speaking for my jurisdiction (in the US).