Inherit page id for drupal node
That sounds like fun.

First, a question: In your example, do you mean that the source page is /blue-work, and you're clicking a link on /blue-work to go to node-1? And you want the destination URL to become /blue-work/node-1 ?

If so, that sounds difficult b/c you'd have an open-ended number of different paths and you'd be telling Drupal to behave differently, paying attention to the tail only (and how is Drupal to know what, exactly, is the tail?). I think it would still be possible, though.

Instead, you could go with what currently works: if you click a link on /source-page to go to /destination-page, then this URL works: /source-page/destination-page.  However, I'd sooner use: /source-page?context=destination-page.

Regardless, you might start with hook_page_alter so you can edit all the links on the source page before it's rendered, adding the source page's url to (the end of) the links. 

Then, of course, you're going to have to check the requested URL to get the 'source-page' context and apply it. Perhaps with hook_page_alter again.