For some first stages and second stages, and some failed launches, their fate is to burn up in the Earth atmosphere. Once the stage has broken into thousands of smaller parts, aerodynamics changes. How? What happens to these pieces?
Most first stages are jettisoned at a relatively low velocity and will simply fall to Earth. In most cases this means destruction of the first stage by falling in the ocean. In some cases (especially Chinese rockets) the first stage may end up landing on land. https://pauldmaley.com/sd1/
Second stages either burn up or are cast adrift in orbit. Any rocket stage that ends up at high sub orbital velocity is likely to disintegrate due to frictional forces which will reduce much of the stage to particulates comprising of iron and aluminium oxides. Such fine particulate matter will generally end up in the ocean hours or days after the launch.
First stages are usually dropped much earlier and don't necessarily 'burn up' when falling back to the planet.
The stuff that does actually burn up, upper stages, satellites and other debris, breaks down into not just smaller parts but right down to fine particles as well.
This Scientific American article "How Much Air Pollution Is Produced by Rockets?" article claims that:
at least 50 percent of a given debris object will end up as RSPs(Re-entry smoke particles) during re-entry.
It further mentions that exact mechanism of this melting-vaporizing-dust creation process is unclear (Not studied). The article is from 2017 and the author of the relevant section in this report might be a good starting point.
Many spacecraft that are deorbited are aimed for Point Nemo in the South Pacific Ocean.
The area is nowadays known as a "spacecraft cemetery" because hundreds of decommissioned satellites, space stations, and other spacecraft have been deposited there upon re-entering the atmosphere, to lessen the risk of hitting inhabited locations or maritime traffic. The International Space Station (ISS) is planned to crash into Point Nemo in 2031.
It is used because it is the furthest point from any land and relatively lifeless due to a lack of nutrients.