I would like download the back up website file from goDaddy, but my subscribed plan has been expired. Seeking for advise how to do, do I need to renew the plan? Or there is a way to download the file even though the plan expired?
The only way to renew a plan is if the plan is current. Renewing an expired plan will not bring files back! It may have the exact same domain name for example, but you have to understand that it will be a totally new domain.
A backup should have been done before your site expired. There is only a very small window of time that support can rescue files after a site has expired, but before that disc space on the server is overwritten with AuntyBrownsKnittingPaterns.com.