In most cases, the property owner rather than the city is responsible for fixing the sewer lines running from their property to the public main in the street. This is often the case even when damage to the pipe is at the sewer lateral, which is outside the property. Unfortunately, homeowners insurance will rarely cover sewer line repairs or replacement unless the part of the line which is on your property is damaged by something unexpected or sudden. If there's a sewage backup or chronic issue, you'll likely have to pay out of pocket for repairs.