for Magento 1, there was a PHPList extension on Magento Marketplace: https://marketplace.magento.com/magemagic-mm-phplist.html
As you might know, the support for Magento1 will end in June 2020 and shop owners will have to migrate to Magento 2, which requires new plugins. They cannot be converted to Magento 2 automatically.
Are there any known existing solutions for the integration in Magento 2?
Embedding an ajax subsription form on a page is not the topic here, I am thinking about a seemless integration of the subscription management in Magento checkout and customer account (if existing).