You are talking about Germany. There and in many other countries there are two distinct meanings of “insurance”: Is an innocent victim protected from damages, and is the person responsible protected?
In Germany an insurance must alwaysalmost always protect an innocent victim. As long as there is insurance (and it doesn’t stop if you missed payment for a month or two, and when it stops the insurance company will call police to your home), if the victim is not a third party (but insurances have paid for damage to family members when it is good for their image), and if the damage wasn’t caused intentional. In neither case does it matter who the driver is.
On the other hand, the insurance company can try to get their money back from the person responsible. Relevant to your question, that would happen if a car thief causes damage, or you lend your car to someone who doesn’t have a driving license or is drunk. Or your dad lends your car to his mate (which he likely had no right to do).
And the person in trouble is the person who caused the damage, not you. So the car thief, or your friend if he lied to you and had no insurance. Your only cost is that the insurance premium can go up which happens whenever the insurance company has to pay out (and cannot recover the money say from the car thief). You can sue the person responsible for damages.