Earlier quoted context omitted.
How does this fraud work? They buy the goods, and provide the seller some random individual's (your) identity?
I have no idea. There are, however, many official invoices (notas fiscais) being issue in my name. I believe there might also be fraudulent credit cards issued in my name that ate being used, or something like that, which would explain the physical retailers not questioning the purchase. That is why I am expecting fallout from this.
However, HIGHLY unlikely they issue a card in your name and purchase stuff in your name online. If they have a card with them, they’ll go to physical stores and leave with the product with them immediately.
Typically (as I said above) they have purchased a stolen CC number online and are using it until it gets blocked or run out of balance/limit.
In any case, there’s zero fallout for you, the victim. These retailers are used to this (0,5% of transactions turn into fraud), so they’ll eventually figure out it’s fraud and they know it wasn’t you. They know you’re a victim too.
[0] https://registrato.bcb.gov.br/registrato/
Edit with the link