Probably in much the same way that a signifigant portion of the colosseum now resides in Rome’s many churches.
CC
The masonry from the Circus Maximus (which started out with wood risers/bleachers for the crowds, replaced after the 1st c AD great fire) probably got carted off for construction. That was a problem even during the imperial period, a continual series of prohibitions on using public buildings as quarries was issued. The coliseum was rebuilt at least once after a quake I think.
The short answer is: earthquakes and popes, in that order.
For much more on the life and death of the Colosseum - and many other fascinating facts about the classical world - check out my book “Naked Statues, Fat Gladiators, and War Elephants: Frequently Asked Questions about the Ancient Greeks and Romans.”What happened to the missing half of the Colosseum? | February 6, 2021 | toldinstone
We owe the Roman poet Martial a debt of gratitude for recording so vividly the gladiatorial battle that took place on the opening day of the Colosseum. It was a battle for the ages - with an unexpected outcome. From the Series: Eight Days That Made Rome.The Story Behind the Colosseum's Greatest Battle | February 8, 2019 | Smithsonian Channel
The Pantheon in Rome was converted to a church, and was in its day and remains to this day the largest unreinforced concrete dome in the world. Other than missing statuary, it wouldn't have been profitable to demolish it, not really any bldg materials that could be recycled.