Why?

Most RDF stores are quad stores these days. Some of them implement extensions like Construct Quad that allow SPARQL to return quads.

The DESCRIBE SPARQL form works nicely to return resource descriptions as triples (even if it's informative and the result can be implementation-specific). But it cannot return quads in the way Construct Quad does.

Previous work

Not that I know of.

Proposed solution

I think it makes sense to have a new form of DESCRIBE that would return quads. For example, DESCRIBE GRAPH :) Not sure about the exact syntax -- maybe smth like this:

DESCRIBE GRAPH ?smth
{
  ?smth ?p ?p
}

Jena's DESCRIBE implementation collects the description from both the default and named graphs - and then returns them in the default graph if quads were requested.
DESCRIBE GRAPH would instead return quads: i.e. the same triples as 1.1 DESCRIBE would, but without stripping the graph URI (of the graph where that triple was found).

More context: https://lists.apache.org/thread/49spskzf3or2ty743yz9p08twzv9p5cj

Considerations for backward compatibility

None?