Flying Without Insurance: Don't Be Stupid

If you are still in your sidewinder and have not put many credits into upgrades on it, you can fly without insurance. I give you permission. Once you have a new ship and upgrades, paid for with your own hard-earned credits, don't be an ass hat and fly a mission without the necessary credits to buy it back when it gets blown out from under you. If you do not have the insurance money to buy it back, that ship is lost to you.

This is really simple, pilot. Before you spend a bunch of credits, or fly a risky mission, look over at the right-hand HUD to the lower left portion of the STATUS TAB. There you see "balance" and "rebuy cost" (the insurance needed to buy your ship again). If your balance is less than your rebuy cost, DON'T spend the credits, and don't fly risky missions that might get you killed. Run some safe, low risk missions to build up your credit balance, or use one of your less expensive ships for which you have enough credits.

What Happens?
If you are not able to rebuy your ship, you will be given the option of selecting a ship you have in storage, or, if one is not available, you will be put into the trusty Sidewinder.

Loans

If your ship is destroyed, and you do not have the credits to cover the amount needed to rebuy it, you might be offered the option of taking out a loan to cover the rebuy. The amount of the loan you can take depends on your highest rank in Trading / Exploration / Combat. The loan is paid back by taking 10% of the profits made from credits you earn.

See the details here:

Elite Wikia Loans