You are assuming that Person A is capable of taking the job that Person B vacated. That may or may not be the case. Inevitably, there will be come cases where Person A isn't suitable for the position.
You do realize that we are not talking about three specific persons, right? I will grant you that at any given time there are people who are unemployed even when there is demand for labor, because for some reason or other they do not fit the available positions, right at that moment. Being unskilled is certainly a factor when it comes to that. But I remain highly skeptical of the mechanism described by the grandparent. If wages were to increase at e.g. Walmart and grandparent was right, it would mean that skilled people would leave the jobs they are already doing to come to Walmart to work. Now, maybe the people laid off at Walmart don't have the skills to fill these now vacant positions, but presumably they must still be filled somehow. Which means that either the employers must accept less skilled labor to do the same job or they have to do what Walmart did, and offer higher pay to attract the right workers.
I will also grant that as wages rise, certain jobs simply cease to exist, because it becomes uneconomical to pay anyone to do them. Being from Denmark where wages are very high, I was astounded to be greeted by not fewer than ten clerks in a small, mostly empty Swatch store I visited in Beijing. To have that much staff to do mostly nothing can only happen where wages are extremely low. If wages were to rise, one by one those clerks would probably be laid off. But not because a more skilled person would claim their position, but simply because it would become too expensive to pay any person to do that job given the value it creates.
I don't think you can assume that the position will be filled. The position may be no longer be economically viable at higher wage rates or lower skill levels and thus be eliminated.
However, there are some additional factors that complicate this picture. If there are fewer unskilled jobs, people will adjust by working to become more skilled. If people have higher paying jobs they will spend more, producing more jobs. If there are many unskilled people looking for work, there is incentive for somebody to find a way to make use of that resource.
But really, the only point I sought to make here was that your original comment which didn't look at the non-skilled worker was missing a bit part of the equation, and so its logic didn't work.
