Nephi divided the kingdom between the prophetic line (descended through his brother Jacob) and the kingly line (descended from Nephi). Jacob’s line maintained the plates. Nephi’s line maintained the kingship and called themselves after Nephi. The prophetic line used whatever name they were given at birth, with no need to retain Jacob’s name. The direct line from Jacob (Nephi’s brother) ended with Amaleki. In his day two things happened. He would die without an heir (Omni 1: 25) and the plates they had been maintaining were filled and there was no more room to add to their engravings (Omni 1: 30).
It apparently did not occur to any of those who descended from Jacob that the Small Plates of Nephi could be expanded by adding additional plates. (See e.g., Jarom 1: 2; Omni 1: 30.) There is no explanation for this in the small plates. Perhaps there was an oral tradition (see, e.g., Omni 1: 9) with Nephi instructing that no more plates were to be added. That would account for the plates being "full" at the time of Amaleki, because none could be added.
In any event, when the plates are filled, Jacob’s direct line ends. I do not believe this is a coincidence. The convergence of these two events is what puts the small plates into the hands of King Benjamin, and in turn through his descendants, into the hands of Mormon. (Words of Mormon 1: 3.)
Amaleki was impressed with King Benjamin’s efforts on behalf of the Nephites. He described King Benjamin as one who labored “with all the might of his body and the faculty of his whole soul.” As such, he was able to convert the people back to the Lord. (Words of Mormon 1: 18.) However, in accomplishing this, King Benjamin had to “use much sharpness because of the stiffneckedness of the people” (Id. v. 17) as he and other prophets preached repentance (Id. vs. 17-18.) Apparently King Benjamin had no problem with others who preached repentance to his people. (Id. v. 18.) Instead he welcomed these “prophets” who taught repentance.
In many ways King Benjamin is the perfect leader, both civic and religious. It is no wonder the lines divided at the time of Nephi and Jacob would come together again in the person of King Benjamin.