I've been thinking about this for a while, since we haven't had any significant closure to the stories of Connor, Shay, Arno, or Aveline for that matter, and it seems that Ubisoft doesn't plan on providing it anytime soon. Though it is not complete, my theory (I call it a theory and not a hypothesis because I believe there is enough evidence behind it; I call it mine because to my knowledge I am the first to come up with many of its aspects) explains many events in the story of the Assassin's Creed franchise.
After the events of Assassin's Creed III, Connor returns home to the Homestead from his trips to New York City on Evacuation Day and to Kanatahséton when he found out that his people had moved westward. He ponders what the frontiersman at the village told him, that congress had granted the land to a man from New York. After months of investigation, he discovers that the village's new owner is a Templar, Shay Cormac, who purchased it for its connection to the Precursor Civilization. He eventually hunts him down by 1812 and kills him.
During the War of 1812, Connor takes part in naval battles against the British using the Aquila. He meets new friends in the Midwest. Later, he meets his wife, a blonde woman, and has several children with her. The Templar Order catches wind of Shay's murder, and a witness informs them that it was Connor who killed him. They send a posse to the Homestead to get their revenge. He and the Homestead's residents successfully fend them off. After about three more attacks, all increasing in number of men, David is killed in battle, and Terry is wounded. Connor decides that the Homestead is no longer safe, and sends his wife and children to his friends in the Midwest (this explains Desmond's patrilineal line being in the Midwest during the nineteenth century, as shown in this AE file; it also explains Connor's wife and children leaving him as it says they do in the Abstergo Entertainment Employee Handbook), but he stayed as he needed to defend the rest of the residents, as well as maintain the Homestead as an Assassin hideout. A huge wave of dozens and dozens of Templars, including cavalry, laid siege to the Homestead, and a naval force of multiple brigs and a frigate blockaded the harbor, obstructing escape by sea. Connor, the rest of the men on the Homestead, a group of French Assassins who had visited to discuss the threat of Napoleon, and the Assassin turkey fended them off for a few days, while the women--aside from Myriam who helped fight--and children hid in the Manor's basement. The sailors in the harbor boarded the Aquila and broke through the blockade, then set sail for Washington, D.C. to ask the United States government for help, as they owed a debt to Connor for his actions in the Revolution, and several high-ranking politicians knew him personally. US forces arrived the next day, but it was too late, as the Templars had broken through and killed Connor and his allies--though they had not found the women and children in the basement. The US soldiers caught a fleeing Templar and interrogated him, and he admitted that the Templar Order was behind the attack. This led to a purge of Templars from America.
Napoleon acquired an Apple of Eden from Egypt after the French Revolution and soon began his rise to power. Years later, during the peak of Napoleon's prowess, Arno discovers that he had been using the Apple, and takes it from him. Without the Piece of Eden, his hold on his empire begins to weaken and he is eventually captured and exiled to Elba. He escapes and reclaims France, but is defeated again and imprisoned on Saint Helena. Fearing his return, Arno sends an apprentice to assassinate him, and he is poisoned and dies of a stomach ailment in 1821.
The reason I did not include Aveline in my theory is simply because I haven't finished Liberation, so I don't know her full story. If you have a theory or hypothesis of what happened to her after the events of Liberation, please comment it.
Please feel free to comment on my theory. Inform me if I missed anything, if I got anything wrong, or if any of my theory contradicts any existing lore. Also let me know if anyone came up with any of this before.