I remember that at the folklore level. Apparently after he had been pierced by arrows and he was incapacitated, his head was hanging down and it needed support.
Bhishma preferring the pillow of arrow over Kauravas ordinary pillows is present in Mahabharata, Bhishma Parva, SECTION CXXI.
Then Santanu's son Bhishma of righteous soul addressed the Pandavas and the Kurus who having reverenced him thus, stood before him. And he said,--Welcome to you, ye highly blessed ones! Welcome to you, ye mighty car-warriors! Gratified am I with your sight, ye that are the equals of the very gods.--Thus addressing them with his head hanging down, he once more said,--'My head is hanging down greatly. Let a pillow be given to me!--The kings (standing there) then fetched many excellent pillows that were very soft and made of very delicate fabrics. The grandsire, however, desired them not. That tiger among men then said unto those kings with a laugh,--These, ye kings, do not become a hero's bed.--Beholding them that foremost of men, that mightiest of car-warriors in all the worlds, viz., the mighty-armed Dhananjaya the son of Pandu, he said,--O Dhananjaya, O thou of mighty arms, my head hangeth down, O sire! Give me a pillow such as thou regardest to be fit!--'"
The Mahabharata - Volume 5
Chapter 975 (115)
The great-souled Bhishma, Shantanu's son, spoke to them. 'O immensely fortunate ones! Welcome. O maharathas! Welcome. I am delighted to see you. You are the equals of the immortals.' With his head hanging down, he greeted them. 'My head is hanging down. Please give me a pillow.' The kings present there brought many soft and delicate pillows that were excellent. But the grandfather did not accept them. The tiger among men laughed and told those kings, 'O kings! These are not appropriate for a hero's bed.' The best of men then saw and addressed Pandava, the maharatha of all the worlds. 'O Dhananjaya! O long-armed one! My head is hanging down. Give me a pillow that you think to be appropriate.' He honoured the grandfather and grasped his giant bow. With his eyes full of tears, he spoke these words. 'O best of the Kurus! O supreme among those who wield all weapons! Command me. O invincible one! O grandfather! I am your servant. 'What can I do for you?' Shantanu's son replied, 'O My head is hanging down. O best of the Kuru lineage! O Phalguna! Give me a pillow. O brave one! Quickly grant me one that is appropriate for this bed. O Partha! O mighty-armed one! You are the best of all archers. You know about the dharma of kshatriyas. You possess intelligence and qualities.' Having been thus addressed, Phalguna quickly prepared to do as he had been instructed. He grasped Gandiva and arrows with drooping tufts. He took the permission of the great-souled one who was the middle one of the Bharata lineage. He shot three extremely forceful and sharp arrows and supported the head of his senior. Bhishma, the best of the Bharata lineage and learned about dharma and artha, was satisfied and praised Dhananjaya for having given him that pillow. Kunti's son was the best of warriors and brought delight to his well-wishers. He spoke to him. 'O Pandava! You have done well by giving me something that is appropriate for this bed. Had you done otherwise, I would have cursed you in rage. O mighty- armed one! This is the way in which kshatriyas should remain established in their dharma and sleep on a bed of arrows.'