If it is clear that the incident was an intentional assault, there might not be any possibility of coverage, and thus no duty to defend. The key factor is the language of the policy. For example, in most auto policies, the defense costs are in addition to the amount of liability coverage. The term is pretty self explanatory the amount of liability coverage declines, dollar for dollar, with each expenditure of legal costs. These are important terms and they govern virtually every insurance policy.
Every policy has an effective time limit.
For example, a policy may provide coverage between January 1st and December 31st of a given year. Once again, simple examples help make the point. Say you have an occurrence policy in force between January 1st and December 31st and the incident in question occurs on October 30th. A lawsuit is brought two and a half years later. The policy in force during the year of occurrence is the one that will offer coverage.