Let's say an open source software project has a component which could be useful as a standalone project. Examples could include Django's event signalling framework, which could be useful for other Python projects or the client components of Postgres, which are not-quite-common with the HAWQ and Greenplum projects incubating at Apache.
After being given a separate existence these components would then (probably) become an upstream dependency of the project they were originally part of. I have been trying to find examples of this pattern but have been unable to, maybe because I just don't have the right terms to search for.
Has this sort of thing happened often enough that there is a term for it?
What notable examples are there of this being attempted?