We have left the US permanently this year. What steps are needed so that the IRS knows another tax return will not be submitted by us in the future? If we have a refund or owe taxes this year, will we still need a US bank account and/or US mailing address? We are not US citizens. Thanks for your help!
There are no steps needed for you to inform the IRS not to expect another tax return from you. The IRS expects tax returns from individuals that have earned income in the US. They know when income has been earned based on tax forms submitted to the IRS such as W-2's, 1099's, K-1's etc. If you have earned income in the US during 2021, you will need to submit a tax return.
Although a US bank account would keep it simple for a refund or tax due, there are ways around not having a US bank account. Here is a useful article addressing this issue: http://blog.sprintax.com/get-tax-refund-without-us-bank-account/
Lastly, you are not required to have a US address to receive a tax refund. If direct deposit is not selected, then the IRS will mail a refund to the address on the tax return. Here is an IRS link to help you navigate this issue: https://www.irs.gov/individuals/international-taxpayers/helpful-tips-for-effectively-receiving-a-tax-refund-for-taxpayers-living-abroad