Should badgus data be erased after a deadline?

An email is being drafted to send to former badgus users asking if they want to download a backup of their personal data. But what should we do with unwanted data? Or even with data that has been requested? Should it be saved (somewhere) indefinitely or should it be erased permanently after some deadline? Should we ask users if they want to delete their data or just tell them it will be deleted after a deadline?