Micah has founded or been early at six startups that have raised more than $300 million and have exited in excess of $200 million. As a mentor at Techstars, 500startups, and various other accelerators and an advisor to dozens of companies, Micah helps founders understand how to build and scale their businesses through effective business and product development. Micah is also deeply focused on understanding how to make the process of building a company a more fulfilling and happy experience for founders. Blogs at http://learntoduck.net and at https://medium.com/@micah
What's the time differential? If it's a logical next step, it's probably ok. If it's a complete shut down - or an asset sale (which would mean that the email list is owned by the acquiring company) - or longer than say 4-6 months, I would say no.
That being said, if you are in the process of shutting down the first company, there is nothing wrong to asking your users if they are open to hearing more in the future.