A Delaware Domestic LLC is cancelled status. The LLC has a California Foreign LLC.
Is the Californian Foreign LLC legally able to continue in business, if the Domestic LLC is in cancelled status?
The 'California foreign LLC' is not a separate entity. There is one entity, the Delaware LLC, which happens to be registered with the Californian authorities as a foreign (out-of-state) LLC doing business in California.
If the Delaware LLC is dissolved then it doesn't exist. Therefore it can't do anything anywhere. Pretending to carry on business in the name of a non-existent company would be fraudulent.