It starts with Nephi having "Plot Armor." He's an idiot, possibly the single dumbest, most incompetent human being depicted in a holy book. A Drop Bear was attracted to the scene when Nephi was busy rationalizing the cowardly murder and beheading of Laban. You see, cutting the head off a helpless, drunk, unconscious man results in a lot of blood, which attracted the Drop Bear.
The Drop bear went to town munching on Laban's body while Nephi was looting Laban's corpse. The drop bear ended up tangled in the stolen clothing. It was a pregnant drop bear and spent most the next few weeks tagging along hidden in bundles of clothing, eating scraps the lazy, pampered and generally moronic Nephi party left behind. It eventually hitched a ride to the New World with Nephi.
The Drop Bear gave birth to her young in the New world, but her descendants were, like Nephi and his descendants, not quite up to par due to heavy inbreeding. The inbreeding kept them from spreading very far, so when whatever cataclysm came along that magically erased all evidence of horses, Old World grains, iron ore mining, smelting and steel manufacture and all the other anachronisms in the Book of Mormon, the heavily inbred Drop bears, along with all evidence of their existence, were wiped out as well.