Ahm... I dond know what kind of sink do you have, but here we have sink that has a pipe that goes below the sink, and than it turns 90* and goes in the wall. on that 90* turn there is a small part that doesn't turn...
It is som sort of filter, that keeps havy objects (your ring) and preventes them to go futher in pipes.
So it should still be there except if it was a LONG time ago, than it is posible that it was washed away by woter farder to the pipes.
That "filter" can be opened, just unsrew it....
If you don't know what the hell I'm talking about, I can take picture of it and post it...
So... There is still litle hope...
Warning, opening the "filter" is VERY big dirtywork, be carufle...
(sorry for bad english) B)