What happened at Mount Doom?

[Tuor of Gondolin]

However, I believe that when Eru took matters into his own hands, he was preventing further tragedy. Though it would have broken his heart to do so, Sam may have gained hold of Frodo and tossed him in. They could also both fall into the fires. I believe that Eru's intervention finished the quest in a way which would cause no more terrible harm

A sound hypothesis. One can imagine Sam torn, appalled
at Mr. Frodo and his virtual insanity, and also thinking of
Rosie, the Gaffer, etc. But would he have just dispatched
Frodo or fallen in (deliberately) as part of his desperate
effort to get rid of the Ring?
Hmm.