Can an Employer hire a person who puts in a late application?

This depends on who you work for and whether you were qualified for the position.  If you work for a company that has a union or work for a government agency, there may be specific rules that prevent them from accepting the late application absent special circumstances.  Whether there may be a violation also depends on whether you feel they were intentionally trying to avoid promoting you.  I suggest you speak to an attorney or a union rep to further explore this matter.