Oh really? I had never heard that before. What's the basis of that belief?
I don't actually think the Church teaches that she didn't die. The Church only says that after her time on Earth ended she was taken body and soul into Heaven.
Some support for this idea comes in the fact that there is no known grave for Mary on Earth. We know where almost all of the Apostles are buried. We also know (based upoon the writings of Ignatius of Antioch) that the early Christians had a deep honor for Mary as the Mother of God. In his letters to John the Apostle, Ignatius states that he wants to visit Mary with a group of women who can't wait to see and touch the breasts that nursed our Lord.
So, understanding the fact that Mary was held in such honor. It's hard to imagine that her remains were not honored and remembered. You can go to the Vatican and just outside the wall and you will see were the final remains of Peter and Paul are. But, you can't find Mary anywhere.
Catholics have the Holy Scripture and Holy Tradition. The Tradition tells us that the apostles were gathered around Mary when the time came, and she was taken to Heaven. They could not find her body nor any bones nor anything to bury. The site of her "dormition" or falling asleep is still a place I think that you can visit in the Holy Land, although I have never been and so I don't know first-hand. I believe there is a chapel or church of some sort there. Others will surely know more than I do.
Also, the fourth Glorious Mystery of the Rosary is the one where we contemplate Mary's Assumption as we pray.