In general, a project must be approved and the permit issued before the actual work can begin. The California Building Code does allow an exception for emergency work if City Hall is closed when the event occurs. This is applicable only if the emergency is of such a nature that repairs must be initiated or life and/or property would be threatened. A permit for such work shall be applied for on the next business day.
We will issue a demolition permit in certain cases. Usually, it is issued for specific structural exploratory work, where certain elements need to be exposed to determine the level of repair or reconstruction necessary, for inclusion into the submitted plans. Another situation is the demolition of an entire structure, which is often allowed before the permit for the replacement structure is approved and ready to issue.
If you have a particular situation where you feel demolition might be appropriate before the project is actually approved, it will be considered on a case-by-case basis. Please be advised, however, that these cases are the exception rather than the rule. The multitude of factors and departments that are often involved in an alteration often preclude anything but specific, monitored areas of demolition.