The amount payable to the rental company in the event of an accident is called your “excess" or "liability” or (in the US) "deductible". Rental companies offer Collision Damage Waivers (CDW) which reduce your excess from the full value of the vehicle in the event of an accident. CDW reduces your excess to €/£/$0 (this is typical in the USA and Canada) or to approx. to €/£/$1,000-€/£/$3,000 (this is the case in Europe, Australia/New Zealand and all markets except North America). To get that remaining excess down to €/£/$0 the rental companies sell "Super CDW", "Super LDW" (includes CDW & theft). There are lots of different names (e.g. in Australia & NZ it is called "excess reduction") but they serve the same purpose.
RentalCover.com offers cheap alternatives to "Super CDW" and "Super LDW" and covers all types of damages caused by an accident.