Using the Project Status field to provide different levels of access to old projects.
Configuration
Project Status Field
"Archived" Status Property Details
You have two main choices for properties of the "Archived" Status. Choose whichever is most relevant for your organization's needs.
Sample Project
End Date a while back. Decision made. Project Status == Closed.
Note: this example is configured with the "Visible to Owner, Manager, and Admin" option selected
Showing on the Home Page for all Users
Swapping the Project Status to "Archived"

Visible to Administrator
Adele (Test User without Ownerships, Admin, or Process Manager rights) cannot see the case.
Administrator (Owner & Process Manager) can still search and see the case.
Deleting
If you'd like to fully hide the business case or project use the Delete button.
Warning: to undo delete you will have to access the SQL DB and run a query.
*You need Admin access to run this query*
You will need to know the "businesscaseid" or "projectid" to run the query. In the query editor within Azure SQL database, you can run the following to find the case or project you want to recover:
(example finding a deleted project)
SELECT Id,Name,isDeleted FROM [epj].[Projects]
Once you've identified the Id for the project, you can run the following query to set the value "isDeleted" to false:
(example recovering a deleted project)
UPDATE [epj].[Projects]
SET isDeleted = 0
WHERE Id = {the project id from the first step, without parentheses}