Yes. You can get student loans for the remainder of the cost of a semester if financial aid doesn't cover the whole thing or if you no longer qualify for financial aid. Be very careful, read the fine print, and make sure you check out as many loan agencies as you can before deciding though, or you could get stuck with a debt that you can't pay back and will ruin your credit.
You can still get a student loans after financial aid pays for your school. However, this will vary depending with the school you are enrolled to and whether there is a remaining balance that the financial aid does not cover.