Unsolicited Application could mean two things.

The first one is in the insurance field. Unsolicited application is a life insurance coverage request made by the individual instead of the broker or the insurance agent. These unsolicited applications are examined closely by the insurance company for prospects of self-selection or the act of individuals seeking insurance but have lower risks instead of seeking insurance through an insurance professional.

The second meaning of unsolicited application is the submission of application for something that is not advertised or available yet. For example you are a job applicant and you have submitted a form for a job position that has not yet been vacated or available at the time of submission. Numerous companies accept unsolicited applications for future references.