Has anyone ever thought of creating a 'Writers Pool'?

I was wondering if anyone here has ever thought of creating a 'Writers Pool'? I'm not sure about anyone else, but I've been writing stories for quite some time, and have quite a bit of stories that I've started but for one reason or another, have shelved. Some of my longer ones may end up as stories when I can get my muse to work them in but I do have some really good starts but have lost interest in continuing.

The aforementioned is why I bring this subject up. Often, if another writer is struggling for something to write, and their muse may have decided to take a vacation, they can either read or draw inspiration from another author's written piece. Granted, the style may differ slightly from what they use but the idea would still create a spark of inspiration for them, and a decent writer can adapt the story into their own.

I guess it would be much like when you were back in school and your teacher wrote a paragraph or two on the blackboard and assigned the remainder for you to finish. I know that often, writers are very 'protective' of their stories but if you have started something and have no real intention to finishing it...why not share? Think of it in this way, it would be like raising your child and sending them off to make their way in the world..perhaps another author can create the 'next big thing' from your 'lightning in a bottle'.

Any thoughts?