I know it is fascinating to find out how did Nagarjuna died but I think his death has little consequence to Buddhism when compared to when he was living. Here's an interesting hagiography of his life that I found great pleasure in reading and learning:-
Nagarjuna (klu grub). An Indian master of philosophy and a tantric siddha. One of the Eight Vidyadharas; receiver of the tantras of Lotus Speech such as Supreme Steed Display. He is said to have taken birth in the southern part of India around four hundred years after the Buddha’s nirvana. Having received ordination at Nalanda Monastery, he later acted as preceptor for the monks. He knew alchemy, stayed alive for six hundred years and transformed ordinary materials into gold in order to sustain the sangha. At Bodhgaya he erected pillars and stone walls to protect the Bodhi Tree and constructed 108 stupas. From the realm of the nagas he brought back the extensive Prajnaparamita scriptures. He was the life pillar for the Mahayana, but specifically he was a major exponent of the Unexcelled Vehicle of Vajrayana. Having attained realization of Hayagriva, he transmitted the lineage to Padmasambhava.
--from the Rangjung Yeshe Glossary
Nagarjuna (klu sgrub) In accordance with many prophecies found in both sutras and tantras, Nagarjuna; (klu sgrub) was born in a Brahmin family in the south Indian land of Beda. An astrologer predicted that in the best case (if he practiced the dharma), the child would live for no more than seven years. When seven years were almost gone, the parents sent their son away on pilgrimage with a servant, because they could not bear the thought of seeing his corpse. However Nagarjuna reached Nalanda and meet Saraha who told him that he could escape death if he were ordained as a monk. Nagarjuna also receive the initiation into the mandala of Amitayus and practicing the mantra recitation through the last night of his seventh year, he could free himself from the fear of death. The following year Nagarjuna received the initial monk ordination and became proficient in all the branches of knowledge in both the Hinayana and Mahayana sutras. Saraha also gave him many teachings upon the secret Mantrayana.
Having mastered all these teachings Nagarjuna returned to see his parents again. He then took the full monastic vows. Once, a terrible famine broke out in Magadha and continued for twelve years. Saraha asked Nagarjuna to provide for the monks of Nalanda who lacked all necessities. Nagarjuna decided to find out how to make gold. He took two sandalwood leaves and, with the appropriate mantras, gave them the power to instantly transport a person to wherever he wished to go. Holding one leaf in his hand and concealing the other in the sole of his sandal, he traveled across the ocean to an island where a famous alchemist lived. Nagarjuna requested instructions in the making of gold. Now the alchemist realized that Nagarjuna must have come across the water by a secret technique, so hoping to acquire this secret he said, "Let us exchange either our crafts or our wealth." "We should exchange our crafts," answered Nagarjuna, and gave him the leaf he held in his hand.
The alchemist, thinking that Nagarjuna was no longer able to leave the island taught him how to make gold. Then Nagarjuna, by means of the sandalwood leaf he had hidden in his sandal, returned to India. There he turned a lot of iron into gold and provided the whole Sangha with all their needs. Later Nagarjuna became abbot of Nalanda. He repeatedly defeated all his opponents, both the heretics, such as Shankara, who ridiculed the Madhyamika view and the shravaka who asserted the invalidity of the Mahayana. Some Nagas came to attend to Nagarjuna's teachings and requested him to visit the Land the Nagas. Having taught the Naga King and his subjects, Nagarjuna returned with the text of the Prajnaparamita in One Hundred Thousand Verses and its abbreviated form. With these scriptures he revived the Mahayana tradition. He himself composed many treatises elucidating the view of the Madhyamika and setting a reference point to the whole Mahayana philosophy on relative and absolute truths.
In accordance with the prediction of Arya Tara, Nagarjuna went to leave and teach in South India. There, too, he composed many treatises. His teachings on Vinaya were equaled to Lord Buddha's First Turning of the Wheel of Dharma, his teachings on emptiness to the Second Turning, and his Collection of Praises (such as the Praise to the Absolute Expanse) to the Third Turning. Once a young prince, who coveted his father's kingdom, was told by his mother, "Your father's life is linked to that of Master Nagarjuna who himself attained eternal life. Therefore, you will never rule the kingdom." Later not bearing her son's unhappiness, the queen added, "Nagarjuna is a Bodhisattva, if you ask him for his head, he will give to you." The prince did accordingly, and Nagarjuna consented to give his head. But although the prince struck with his sword again and again, the master's neck could not be severed. Nagarjuna said, "Once when I was cutting kusha grass I cut off the head of an insect.
The karmic consequence of this act can still affect me and you can easily kill me with a blade of kusha grass." The prince tried and at the first stroke the masters' head fell on the ground. Milk, not blood, poured out and the severed head spoke: "I shall now go to Tushita heaven, but later I shall return in this very same body." Afraid, the prince, threw the head far away. However both the head and body of Nagarjuna turned into stone and it is said that the head, slowly but surely, moves closer to its trunk and that eventually, when the two reunite, Nagarjuna will revive and perform vast deeds for the benefit of the Doctrine and beings. Nagarjuna had four principal spiritual sons, Shakyamitra, Nagabodhi, Aryadeva, and Matanga, as well as three close sons, Buddhapalita, Bhavaviveka, and Ashvagosha.
