Elance used to have a great feature that allowed you to see which freelancer was awarded a project you'd placed a proposal on and what the amount of the winning bid was.
As far as I know, Upwork has never provided this very useful information.
Clients have the option to update the job post as closed once they hired a freelancer already. However, some clients leave jobs open even after they have hired somebody in case they want to hire more than one person. You can click View Job Posting from your proposal page and see if anybody's been hired in the Activity on This Job section.