It depends on the cost block: acute treatment in EU countries is covered by the statutory health insurer via the EHIC – but only at local standards and at public facilities. Outside Europe, the fund generally pays nothing; here only private international health insurance steps in.
Medical repatriation to Germany is never a statutory benefit – it is covered exclusively by international health insurance. Permanent accident consequences are compensated by your private accident insurance with a lump sum, worldwide and around the clock. If someone else caused the accident, they are liable under the law of the accident country – legal protection insurance with foreign coverage helps with enforcement. The complete overview of all cost bearers including a checklist for the first 48 hours is in the guide Accident Abroad: Who Pays?.