I come from the Physics site, but I can imagine this is happening in the other sites too. Very often a question is closed, and I highly respect the work of the moderators because they maintain the site clean from a lot of rubbish that otherwise would ruin it.
But sometimes a question receives a lot of upvotes, and nobody can deny that this is because, although out of scope, it is highly interesting for the typical user of the site.
So, for example, somebody asked "What are the papers every physicist should read?". I upvoted, because the answers were incredibly interesting for me as physicist. In fact, I have already read two of the recommended articles and, well, I wish I had read them before...
This is my proposal: when a closed question receives more than X upvotes, it is automatically moved to a special site. It enters there with a single tag indicating the origin site (for instance, PHYSICS) and remains there, open, with the possibility of receiving new answers.
That threshold number for the question to be migrated had to be proportional to the number of users of the site or to any similar parameter. Well, the details had to be worked out, but that is the idea.
Only automatically migrated questions would be allowed in that site.