I noticed this note on a question that resurfaced:
This question has answers that may be good or bad; the system has marked it active so that they can be reviewed.
Are there questions that are in an inactive, invisible state?
"Active" just refers to the location of the question near the top of the active questions tab. I believe this message is part of the attempt to make the purpose of Community “bumping” more obvious.
Regarding the title question: using this sense of "active", the "inactive" counterpart would be questions that do not appear near the top of the active questions tab. These are fully visible to anyone with the link, available by tag index, and searchable.