Question:
How long after a semester starts will the financial aid office send out funds to the student that was leftover in their account?

Answer:
It varies by school. You should contact your financial aid office. I believe that most schools make funds available quite soon after the start of the semester.

How long after a semester starts will the financial aid office send out funds to the student that was leftover in their account?

Most colleges wait about 2 weeks to distribute financial aid. For instance, this year my college starts on Aug 24, the financial aid that is left over is given out to the students on 11 or 12 September. Ask your financial aid office. FRESHMAN students will not get financial aid until the end of September. Students who are awaiting a Canadian loan or grant also do not get aid until 30 Sept. Make sure you attend your college's financial aid lecture, or you won't get any of your aid.