Also, people with the genetic disease DiGeorge syndrome, often born with parathyroid glands that are too small and can't produce enough parathyroid hormone.
Related to this is pseudohyporparathyroidism, which is where the kidneys simply don't respond to parathyroid hormone because of a genetic defect in the parathyroid hormone receptor.
Lastly, parathyroid hormone increases calcium reabsorption and reduces the reabsorption of phosphate from the kidneys, so more phosphate is excreted through the urine.
Now, even though parathyroid hormone stimulates bone resorption, it's been found that intermittent injections with teriparatide activates osteoblasts more than osteoclasts, therefore increasing bone formation.
If calcium levels fall, the four parathyroid glands buried within the thyroid gland release parathyroid hormone which frees up both calcium and phosphate ions from the bones.