Yes, it needs to be "cleared".
In the database, the resolution field is always present, but holds either (a reference to) a resolution or it is empty, with the content described as "null" or empty. It's not a string saying "nothing here", there really is nothing there, not even a byte, nybble or bit.
Empty, none, unresolved, not there, even the word "null" itself, etc - these are all not null and an issue with these values is resolved because the field is not null, it's got a value.
So yes, the resolution should be 'empty' unless it is in a "Done" (or equivalent) status.
In Jira UI, the best thing to do is use the built in post-function. Edit transitions that go out of "done" status to "not done", adding a post function called "update field". It will ask you which field (resolution) and offer you a list of options (select the first one - "none"). When you save it, there's a bit of discontinuity - the post function will display "clear resolution" rather than "update resolution to none/empty/clear".
If in doubt, make a copy of the default (non deletable) default Jira workflow and edit that, it has the post-functions as examples.
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