For close flags, if nobody handles them in time, will be marked as aged away, as the Meta SE FAQ says:
[Close flags] follow the normal rules for close vote aging:
- The oldest recommend closure flag, once per day, at the following times:
- 4 days after the last close vote if the question has 100+ views
- 14 days after the last close vote if the question has fewer than 100 views
Close flags send a question to the close votes review queue where it is almost always handled by regular users with 3k+ rep and not diamond moderators. You should be able to see if the review has been completed by going to the timeline URL (not linked anywhere) which looks something like this:
https://scifi.stackexchange.com/posts/####/timeline. For example, here, you can see the reviews for the question you mentioned in the comments. Unfinished reviews are not shown in the timeline, and it's not easy to get a link to them unless you can access the close votes queue.
In practice, I only think I have ever had aged-away flags on Stack Overflow. (Close votes are another story.) As you can see on the review page, the queues are always pretty empty. It's pretty easy for close flags to be handled: If one person votes to close, it's helpful. If three people vote "leave open" instead, it's declined.
My advice: don't babysit your flags ;)