Being involved in a brushing scam means that someone has gained access to your name, mailing address, and potentially other information. What else are they doing with it? Depending on how they accessed your information, they could be privy to a lot more of your personally identifiable information than you realize. Other crimes, such as hacking into a retail website where you legitimately placed an order so scammers can get your data, may have led to your information being used in a brushing scam.
If you begin receiving packages that are addressed to you but you did not order, contact the retailer immediately. Then change your passwords on your online accounts, just in case the scammer got your address by hacking an account. If the volume of shipments becomes a problem, such as the case of the victims in Arizona, you can contact the post office for help with holding packages until you can pick them up or otherwise handle the matter.