Hagrid's wand was made of oak. This wood was called the King of the Forest from the winter solstice to the summer solstice. According to Ollivander, oak wood could only be harvested during that period, and it had an affinity with both animals and plants.
Holly had to be harvested at the end of the year. When the days began to shorten again, from the summer solstice to the winter solstice, it replaced oak as the King of the Forest.
Because a Muggle-born girl had died, Hagrid's pet Aragog became a suspect. Hagrid was expelled from Hogwarts, and his oak wand was snapped. Unlike Newt Scamander, whose Dugbog had endangered a student's life but caused no death, he was allowed to keep his mother-of-pearl wand.
Having a wand snapped was like having a bone broken. Even after it healed, you remembered the pain. The crucial thing was that Hagrid could not buy a new wand to replace the broken one. He was so large that he would definitely be recognized and reported if he appeared at Ollivander's. He could only ludicrously hide his wand inside a pink umbrella.
Scamander could use a wand like any ordinary wizard, and no one could tell that he had once been expelled. Then there was Isolt, the founder of Ilvermorny. She had never bought a wand from Ollivander either. Her first wand had been stolen from her aunt, who had used it to kill Isolt's parents before taking Isolt in, intending to raise her according to what she considered proper standards.
Although it was Isolt's first wand, and had taken part in the construction of the first Ilvermorny school, as well as adventures with her Pukwudgie friend and her meeting with her husband, Isolt still buried it after her aunt died. Later, it grew