Then your answer is far simpler, have a box that says "Newsletter" and ask for an email address and a button to say "Add me" or similar. Job done.
No need to have a system to stall the process of leaving a site, me personally, I have come across a few sites like that from web searches, found that they are not what I am looking for and when leaving I am prevented from closing the tab to leave. Utterly annoying.
The problem with these pop ups, its not that they work, its that they pester and these sites have in most cases mega bucks to start with, so that argument alone is no justification in the first place.
You also have a web compliance issue with a pop up for blind, partially sighted and disabled users who will find it difficult to get out of these pop ups or layers.
If these other sites were able to jump off a virtual bridge, would you?
IMHO keeping things simple is best option and allows your page to be accessed by more people than just annoying people as you then have to venture in to the setting of cookies, etc just to remember who is in or out.