If a customer wants that you delete the account you can do so by clicking on the “delete” button in the account details page. The data will be erased from the database and can’t be searched for any more nor restored.
Please remember to remove personal user data also from any 3rd party provider that you are using (e.g. Mailchimp, Google Analytics, etc.).
If the account contained payment data the data is still stored in your payment providers database which you might need to keep longer depending on the accounting rules of your country.