Just a clarification on FinAidOfficer's post above.
Private loans do not become the responsibility of your next of kin if you die. Private loans, just like any unsecured loan, do become the responsibility of your ESTATE if you die. That means that the private loan company can try to collect from the assets in your estate at the time you die--house, bank accounts, etc.
However, if you have a co-signer, the private loans will become the responsibility of your co-signer if you die. My grandmother is my co-signer, but I have life insurance with my mom as the beneficiary. If I die, the private loan company can't go after the life insurance money (true in most states), but they could go after my grandmother. I've set it up with my mom so that the private loan company will get paid out of that life insurance money specifically so that they will not go after grandma.
Additionally, if someone takes out a loan in their name to pay for your school, which you intend to pay, the loan remains in their name when you die and they are responsible for the repayment.
You cannot volunteer other people to be responsible for your student loan debts. The only way that happens is if they sign off on it, either by taking out the loan or by co-signing.
If you die with private student loans in your name only, and your assets don't cover the debt, the private loans are usually forgiven. Though (on these boards) there have been cases where they go after the family, and have even gotten some payment just to stop the harassment, this is an unethical business practice. These boards have shown cases where the family member has to go through (a lengthy) dispute process to get the SL/CA accounts removed, but where they did not have anything to do with the loan, they are successful.