During waxing, all the surface hair is removed and unlikely to have broken in the process. When you wax, hair is removed from the root.
From the diagram, you can see hair in the anagen (growth) phase. That is, the hair immediately beneath the skin that’s getting ready to emerge to the skin’s surface. Any hair you’re feeling is hair at the anagen phase.
Worry not, this new hair growth will be very fine; not coarse at all.
Because the anagen hair had not reached the surface, it was not pulled out during your wax. With repeated waxes, you’ll experience fewer occurrences of anagen hair beneath the skin’s surface immediately after a wax.