One approach could be to store the instance rights before the process and the to restore them at the end of the process.
You can get the instances rights xoging out the user. The down side is that you get all kinds of other fields which you do not need to XOG back in. Preferable you should remove them from the XOG input and leave only the required fields and the instance rights (complete=yes)
You can get only the instance rights with queries, but they are kinda complicated.
If you are talking about the auto right instance manager you could simply specify somebody else at the end of the process.