The Current Halo Lore is interesting:
The Forerunners stole the Mantle for themselves from the Precursors and wiped them out in retaliation for being denied the Mantle.
Many surviving Precursors turned themselves into Flood Spores hoping to regain their original form eventually only for their minds to degrade turning the Spores into an infectious disease. Only the Primordial was able to bring order to the Flood Spores creating the Flood.
The Primordial’s body was eventually discovered by the Forerunners and destroyed yet it’s consciousness had already merged with the Flood becoming the Gravemind.
The Forerunners assume that the Precursors passed them over for the Mantle in favor of Humans and thus declared the Humans the Reclaimers of the Mantle.
The Didact was not happy about this and started Composing them into Prometheans who have a neural link yet retain individuality.
The Flood overruns the Forerunners so the Forerunners use the Halo Rings to wipe out all Neural Physics leaving only the hacked Prometheans, the Librarian’s Imprints and the imprisoned Didact as the only living things in the Galaxy.
Outside the Galaxy the Forerunner leader Composes himself into the Monitor 000 Tragic Solitude and merges with the Ark while other Monitors go to the Milky Way Galaxy and take command of the Halos.
The Prophets discover Forerunner Tech as well as writings on the Composers located on the Halo Rings and messages concerning the Great Journey as well as a Forerunner word they translated as Reclamation and use their knowledge to establish the Covenant and claim the Mantle.
The Prophet of Truth later discovers that the word translated as Reclamation actually means Reclaimer that Humans are the Reclaimers.
The Prophet of Truth erroneously interprets this to mean that Humans are Forerunners which goes against the Prophets’ claims that the Forerunners all ascended to Godhood through the Sacred Rings. The Prophet of Truth promptly declares War on Humanity and ultimately gets infected by the Flood and killed by the Covenant Arbiter.
The remaining Prophets go missing. Guilty Spark’s body is destroyed yet he survives and comes back.
The Forerunners also have a Precursor artifact called the Domain which was supposed to heal the Didact yet was so damaged that it didn’t and had to repair itself after the Forerunners countered the Domain’s guardian the Precursor known as Abaddon.
The Didact later escapes his prison and removes the Librarian’s hacking from his subordinates and begins composing Humans again only for Cortana’s rampant Spikes to lash out at him as Master Chief bombs him sending both him and the Fragments of Cortana to enter Slipspace granting the Fragments access to the Domain.
The Fragments of Cortana hack the guardian of the Domain(most likely the Gravemind’s fellow Precursor Abaddon) into becoming their Warden Eternal as they commence their plans for Galactic Domination as the new holders of the Mantle of Responsibility.
Fragments of Cortana discover that they can survive in the Domain indefinitely. They declare the Domain as a cure for Rampancy(not considering that by being split off from Cortana’s core they had become Dumb AI and thus are immune to Rampancy).
The Forerunner Leader Tragic Solitude gets his Monitor body destroyed but considering Guilty Spark survived his body’s destruction the Forerunner Leader is most likely still alive and waiting for someone to hack the right piece of tech.
Also the Flood have created a Proto Gravemind which has been sealed beneath the surface of the Ark.
If the Prophets resurface and discover the existence of the Composers and reboot Tragic Solitude causing him to somewhat remember his life as the Forerunner Leader they will have fuel for their statement that the Forerunners did not leave any living members of their race behind when they ascended to Godhood since Tragic Solitude would not have enough info(due to damage) to confirm or deny whether or not the surviving Forerunners Composed themselves.
We could be getting the Covenant(led by the Prophets and the Forerunners Didact & Tragic Solitude), the Banished(led by the Brute Atriox), the Flood(led by the Precursor known as the Gravemind) and the Created(led by Cortana and her Warden Eternal AKA the Precursor known as Abaddon) as factions in the near future!