Q:

Can we prevent questions from being closed as duplicates of closed questions?

For example, a question that gets closed as a duplicate of a question that is off-topic is also off-topic. It should either be migrated to an appropriate site, if an appropriate site exists and there are no other problems with the question, or closed as off-topic. Likewise, a question closed as a duplicate of a question that is too broad is also too broad - if it was more specific, then it wouldn't be a duplicate and shouldn't be closed.
I think that following links from closed question to closed question is a poor user experience, especially for new users or people browsing in from search engines trying to get answers. The duplicate feature should be used to point people toward good questions with good answers, not to link 2+ unwanted questions together.
Additionally, it might be a good idea to have tools to check in-site links. For example, if links to other questions are posted in comments or answers, they show up in the "Linked" part of the sidebar. Finding questions that have been linked to that are closed may also be helpful. The links can be cleaned up so that users aren't brought to questions that aren't appropriate for the site, again helpful for new users and people browsing in.

A:

I think both sides of the argument have merits.  
Closing as dup of some closed question is not a good UX if they link to poor quality questions because it gives some merit to both questions and also gives the user some false hope that they might get a good answer.  But at the same time, there are good questions that are still closed as off topic (mostly older, historically significant questions), that you do want to link new questions too.  You also have to take questions that are closed and then reposted by the same poster.  You need to be able to close the 2nd question as a duplicate of the previously closed question as a pointer to the OP that he/she should be fixing their old content and not reasking.
There is also a problem of a question that is closed as a duplicate of an open question and then that open question is closed at a later date.  How would you handle that situation?  Do you want to go back and retroactively change the duplicates to closed?  I have no idea if duplicates are weighted differently than closed question in the question ban algorithm, but if they are, you could unintentionally trigger a ban on someone for something they did a while ago.
Because of the issues, I don't see an automatic way of policing this idea but we could consider doing something manually through a new review queue and/or a new privilege for high rep users (maybe 10K or 20K or a new threshold like 15K)
The idea would be:

If a question is closed as a duplicate of a closed question, then the questions are added to the queue for review.  The reviewers could then decide if the new question is worthy of staying closed as a duplicate, or if it should be changed to a more appropriate close reason.
If a older question with existing duplicates is closed, any question that is closed of a duplicate of the now closed question could then be added to the queue and reviewers would decide what to do with the duplicates (stay as a duplicate or get changed to closed for a more appropriate reason).

