Since angiotensin receptor blockers lower the amount of sodium that your body absorbs is it possible to develop hyponatremia if you don't eat enough salty food (for example maybe you're fasting for one day and drinking only water and your med)?

ARBs often cause high potassium than it does in retaining sodium and water. Our kidneys and brain have a good mechanism to maintain salt-fluid homeostasis in the short term. Causes of clinical hyponatremia include kidney disease, excess beer and bread diet, excessive water drinking and exercise over long periods, cancer, heart/liver failure, surgery, brain disease, and other drugs

Avoiding salt for one day only will not result in hyponatremia. On a normal diet and proper dosage it occurs rarely