We must deal with this doubt. Insurers do not always guarantee car insurance with third party extension. Grace periods give time but expose one to dangers. Accidents happen unexpectedly. You can still put in your claim because your policy has not lapsed. However, insurers are not likely to proceed until you pay up. During an accident claim, late payments, current dues and deductibles, if any, add up to a significant amount. You will need large cash upfront to succeed with your accident claim. Pay regularly to avoid extension on auto insurance hassles.