The Backdrop team has been working together with Tim Otten to provide support for Backdrop CMS within CiviCRM.
As you may know, Backdrop is a fork of Drupal that maintains most of the APIs of Drupal 7 while providing new functionality like configuration management, more powerful layouts, and built-in Views in core. Backdrop is trying to bring down the cost of ownership by shifting Drupal's backwards-compatibility approach. Drupal basically commits itself to drastic changes every few years, while Backdrop is committing to a more WordPress-like approach of minimized API changes while providing new functionality.
Backdrop's primary audience is budget-restrained sites; putting us in the SMB, education, and non-profit space. Basically, the same we hope as CiviCRM. Supporting Backdrop would be a great way to bolster both projects.
As Backdrop is so similar to Drupal 7, we expect the porting to go fairly quickly, though it may result in a lot of similar code to the existing Drupal integration. Considering Backdrop (or Drupal) may diverge further in the future, it's likely that adding Backdrop as a new top-level CMS (e.g. the same as WordPress or Joomla) would be a better long-term approach for maintenance.