They’ll actually keep growing even once the oxygen is gone. What is happening is that the yeast is using the oxygen to build up their sterol reserves. These sterol reserves are depleted when the yeast is growing since in the absence of oxygen both the mother and the daughter cell get half. At some point growth will stop when the sterols in the yeasts are too low for further growth. But that happens quite a while after all the oxygen is consumed. High gravity fermentations need more O2 that regular fermentations since you don’t want the yeast to deplete their sterol reserves too much. If that happens the cell walls get too weak to withstand the rather extreme alcohol concentrations.
In the presence of a lot of sugar, and any practical brewing wort has lots of sugar from the yeast’s point of view, vey little to none of the oxygen is used metabolize sugars aerobically. Even in the presence of oxygen the yeast will ferment. This is called the Crabtree effect.
Kai