Firstly is it possible to attach a single field collection to multiple nodes (so when you opened each node, you'd see the same field collection. If you altered one, they'd all change.)
And secondly, if the answer to the first question is yes, how would you go about doing this? Has anyone ever tried this before?
I've been looking through the database tables and it seems like there's no reason you couldn't just point multiple nodes to one fc, however I can't find anything on the topic.
Brief Example
A quick use case to clarify Geoff's question:
When I create node b, I have the option to populate a field collection from node a rather than a blank field collection.
Editing the field collection on node a, would then also change the value in b.