The debt experience while you are a student can sometimes be taken lightly as you are still working your way up to build your financial stability.
Students study using different financial sources depending on their personal background. Many financing institutions are well aware that while you are still a student, you are most likely dependent or you don't have financial stability like an employed person with a salary.
The answer to your question is twofold. Some institutions can be lenient and give you a loan while you are a student with debt. This also depends on the amount of money you owe and how much money you are borrowing.
On the other hand, other institutions would view your situation as a risk, and would not take a chance to grant you a loan.
However it is not common for a student to apply for a personal, but under certain circumstances beyond the student's ability to cope with responsibilities that require finances, they might take the route of applying for a personal loan.
Financial institutions like banks and other financing institutions require your employment details in order to consider you for a loan. However, each financial institution has its own evaluation standards depending on whether they see you as a risk or potential future client.
Should you find yourself in a situation where you will need a loan as a student but still having debt hanging over your head, visit a financial institution and find how they will approach your situation. Another option is to use the credit score sites that will rate your financial eligibility.