First you would add the checkbox to the data card of the file. Then you could checkout all "Inactive" files and apply the checkbox. If there are a lot of files (thousands), you can apply the checkbox in one of two ways in bulk:
1. Create a workflow transition from "Inactive" to a new state maybe called "Variable Update". In the transition, add an action to change the checkbox, then auto transition it back to Inactive. Then you can select all Inactive files and transition them.
2. If the inactive files are in their own folder, add the Inactive checkbox to the folder card. Then use the "Update values in files" function to push the folder card "Inactive" checkbox status down to all checked out files.
Lets say I have a checkbox on the data card. When checked it has a value of 1 and not checked it has a value of 0 (I think that is how they work). I then go through and set all Inactive files to have a 1. That all seems very clear to me including your proposal on how to do a batch update.
The problem I foresee is that on the search card I will have a check box which can have either a 1 or 0. But this limits the results from showing Active and Inactive simultaneously. I'm not sure this is a requirement but it might be annoying in some instances.
If you're wanting the files to be in the vault but not to be used or seen by anyone then could you not control the workflow state so that only users that you wish to see the files i.e. admin or management can and that everyone else can't?
This means that when they run a search it won't appear because they don't have permissions for the files in that state.
It is more that I want everyone to have the option to not see them. There are instances where it is useful to see what has been previously been made Inactive. I wouldn't say the majority of the time, but not rare enough to justify your suggestion.