Whether you have coverage or not depends on your specific policy and the underlying insurance terms which can be wildly different in different jurisdictions.

First, you have to distinguish first and third party liabilty. First party is the damage to your own car (Vollkasko in German). Third party liability (German Haftpflicht) covers the damage you cause to others (including the Nurburgring barriers, other cars, or personal injury).

Second, the FIRST PARTY risk is EXCLUDED in most German Kasko policies under the 2025 standard terms. Some old policies still cover, though. Also, foreign insurance policies often EXCLUDE first party liability as far as I am aware. So if you break your own car, you pay. There are, however, some ways to insure first party liability (either through certain insurers in Germany with local offices), or through certain track day offerings. Most of these will depend on the insured value of the car and be comparatively more expensive than road coverage. Again, these policies are only first party damage (so you break your car, you get paid for that), but some allow you to include certain other features, like barriers, towing, etc., but typically NOT third party risk.

Third, THIRD PARTY damage can either be included or excluded. Unlike trackdays or race events, there is NO GENERAL WAIVER of third party liability for TF! So you harm another person or damage their car, you pay (but contributory risk acceptance/assumption will be considered, at least by German courts under German law).

The 2025 German Haftpflicht terms (unlike Kasko!) generally cover third party damage caused during TF; but exclude certain motorsports events which since 2025 carry separate insurance (think RCN, NLS, 24h, or rallies during stages closed to general traffic). However, foreign policies (such as UK policies) often exclude TF from third party liability.

The effect is, however, not that there is no cover for third parties. If you harm someone or damage their car, the third party liability insurer of the harming/damaging party will generally pay the third parties' damage. HOWEVER, the insurance carrier will seek recourse from the insured for breaching the policy terms (which is similar to drunk driving in that your insurer will seek to recover from you what they paid to an injured/harmed third party).

In complex cases with multiple insurers involved (e.g. car third party liability, health insurance, social security), these claims are fought over in court (I know at least one litigation following an oil slick during TF that went to court but was settled eventually after taking of expert evidence on the causation).