Rawsie-compressed files are regular DNG files that you can work with in any software supporting DNG format.
Compressed files are always outputted to the destination of your choice or destination defined by your Lightroom catalog and you always have access to them just like to any other files on your desktop or in your cloud. Rawsie has no access to blocking your files, folders or disks.
This means you are not dependent on whether you currently have an active paid Rawsie license or not in order to manage or edit your compressed files, they are yours forever.
If you will not renew your Rawsie license for another year, Rawsie will get defaulted to the free version that allows compressing 30 images a day, that's the only change you would see.