Brokers are not involved in this equation. They are just intermediaries connecting buyers and sellers. It's the option sellers who bear the risk of naked options.
Short options require about 20% margin. If breached, brokers will automatically BTC to cover naked positions (covered puts are not the problem). This scenario assumes that all option sellers ...
It is guaranteed by OCC, if the seller does not full fill the requirement, then OCC will full fill the requirement.
OCC becomes the buyer for every seller and the seller for every buyer, protecting its members from counterparty risk.