Once you have sent corrective tasks, they go to your business partner's inbox (you can also see it in your Outbox, as an 'outgoing' task) - until your business partner takes an action, at which point the task is returned to you in your inbox (awaiting your action).
In general, the task will keep on going back and forth between your business partner's and your inbox until the task is resolved.
In addition to tracking the status of your Corrective Action tasks in your inbox or outbox, you can also go to the 'Corrective Actions' status page on your sidebar :
On this page, you can see the list of all the corrective actions your company has sent, including the resolved ones. If the list is too long, a filter can help you look for the right task(s) based on Corrective Action categories, delivery dates, and several other filters visible below: