People returned to live in Pompeii's ruins, archaeologists say

I think I found the source paper (written in Itallian):

https://pompeiisites.org/e-journal-degli-scavi-di-pompei/la-...

So the archaeologists think that, after the destruction of 79 A.D., some survivors returned to Pompeii and found their homes half-buried in ash. They tried recover their belongings by digging underground, and some apparently attempted to rebuild their lives in their old homes, because they had nowhere else to go.

While their efforts ultimately proved to be futile, they did leave some historical artifacts behind (e.g. bread oven entirely made of salvaged materials), and the archaeologists recently unearthed them.

For those interested, there's a new set of hour-long videos on the PBS site that has more about the recent Pompeii excavations.

There are four so far. Not sure if there will be more: https://www.pbs.org/show/pompeii-the-new-dig/

How would anyone be able to afford anything if all their possessions were under hardened magma

IIRC the first explosion of 79 AD didn't bury the Pompeii completely. (It did bury Herculaneum, and much deeper so.) It was another explosion around the time of collapse of the Western Roman Empire that finished the job and hid the remaining structures from human view.

looters would dig holes at known rich villas?