have you tried using a pair of needle nose pliers to grab ahold of the stuck stay and pulling it out.
If you can't get it out...the other alternative is to just buy some more collar stays at the store to replace the lost one. They sell them in packs at your better retailers and they aren't overly expensive.
For future ref....when washing collared shirts check them before putting them into the machine to wash them to see if they have removeable stays. Some shirts have them stitched into the collar others allow you to remove them. If removeable, it would be advisable to remove and put them back in as you wash and dry the shirt in question because as you've discovered they come out in the machine and end up getting lost.