In a couple of major companies where I worked, I archived all my code before leaving, burned them to CDs, and gave two copies to my manager. And I kept a copy for me. I copied them on my home discs, automatically backed up, and left them there.
In both case, the companies lost the copies, and came back to me offering money - years later. And yes, I took it!
It's a sensible idea to have offsite backups - and taking copies home is a good way to do that. Could be illegal, theoretically, but really, what would you do with this specialised stuff? But it certainly is useful to the original company.
So take copies of all the emails, and leave good contact details with your manager, their manager, and if possible for your replacement, and offer a support rate of - say - double your current rate (don't mention that to your replacement). Make it a daily rate, not hourly.