Final answer:
Copper deficiency is the most likely trace element deficiency to occur in long-term parenteral nutrition (PN)-dependent patients after 3 to 6 months of therapy.
Step-by-step explanation:
In long-term parenteral nutrition (PN)-dependent patients after 3 to 6 months of therapy, the most likely trace element deficiency to occur is copper deficiency. Copper is an essential trace mineral that plays a crucial role in hemoglobin production. Its deficiency can lead to decreased iron absorption and transport, resulting in hypoferremia and anemia.