They did make Symbian open source[1], but I don't think it's still available. And I'm not sure if it was complete. I think when the Symbian Foundation disbanded and Nokia took over (again), they may have done some more work in closed repos.
That explains why nobody is making a new Symbian device today, it does not explain why they stopped around 2010.
Nokia apparently abandoned development so they can make windows 7 phones. Android filled the gap, but android was probably an inferior product before Symbian was abandoned.