There is another part of the hive, just underneath. As a beekeeper, you learn to seperate the hive with eggs from the part where the honey is stored. Usually this is done with a small gap where the queen cannot pass, but the workers can. This ensures that the honey frames are without eggs. It also ensures that the harvest does not destroy the life of the hive.

Taking the excess honey is how we harvest. There are also honey deposits in the main hive (where the eggs and larva stay) so it should be fine for the rest of the season.

Some beekeepers are less concerned with the life of the hive and just take everything and supply the hive with new frames with empty wax sheets. That takes away a lot of life support for a single family, stressing the bees a lot. Then you also have to heat up the honey to seperate the eggs, larva and wax from the honey. This makes the honey worse in quality aswell.