First, if you are on Subscription, you are able to authorize up to 3 releases back. If you are not on Subscription, once you upgrade you cannot reauthorize the previous version. That means that
you will still be able to OPEN 2009, but you will not be able to AUTHORIZE it. However, if your PC dies you will not be able to reinstall 2009 and activate it. If your current PC continues to breathe for years to come...with an authorized version of 2009 already loaded...you'll be able to technically continue to use it to open 2009 project files. 'Course, it is no longer supported, so don't expect any help from Autodesk or your reseller if you have a problem or it kicks the bucket for some reason.