If someone borrows your vehicle your insurance may cover them for injuries, it will depend upon your state's insurance laws as well as the coverages you have as part of your car insurance policy.
For instance if you have Personal Injury Protection (PIP) then it typically covers the Policyholder, policyholder’s relatives in the same household, passengers , other authorized drivers and the policyholder and family members if they are injured while riding in someone else’s car or as a pedestrian when struck by another vehicle (in some states).
Thus with PIP coverage if the person borrowing your car is considered an authorized driver their injuries should be covered. But in many states if the person you loaned the vehicle to has their own car insurance with PIP coverage it instead would be used for their injuries instead of your auto insurance.
Speak to your car insurance agent to find out what exactly your insurance policy would cover when letting someone borrow your car.