In Grand Theft Auto Online you can insure your cars by taking them to any Los Santos Customs shop. You cannot get insurance in the story mode for Grand Theft Auto V.
Full coverage is located in Loss/Theft Prevention options. It is unlocked after purchasing a Tracker for your car.
If your car is stolen, explodes, or otherwise wrecked, you can then make a claim and get a replacement for a small fee. You will not lose the mods and customizations you put on it.
Detailed explanation[edit]
Insurance is purchased at Los Santos Customs in the online mode. If your car is destroyed or stolen you can make an insurance claim by calling the insurance agency and they will deliver you an exact copy as long as you can pay a small premium.
If playing in story mode there is no insurance. You can store any modified cars in your characters garage at either your safe house or a purchased garage. If you take these cars out and don't put them back, they will be impounded and you have to pay a small fine to get them back. The only exception to this rule is the story characters personal cars. These cars ( and Franklin's bike ) will always be near you when you spawn. Franklin for example has the car you drop Lamar off in after delivering the two cars to simion in the first mission.
Garage ownership works the same in online mode as offline story mode. Same with the impounding except after a while the police will destroy your car after a certain period of time, and you must steal it back rather than paying a fine.
