Should web developers specialize or generalize as they grow in their careers?

Is it better for full stack web developers to specialize or generalize as they grow their careers over time?

Having a working knowledge of the full stack, generalists are flexible and versatile across the stack and across languages and frameworks, but they may lack deep knowledge in any particular area and may not be able to handle the more challenging requirements in a given area.

Front-end and back-end specialists have deep knowledge in their area, but do they paint themselves into a corner if their chosen specialization (e.g. framework, stack, etc.) falls out of fashion?

How then to develop deep knowledge in a specialized area as well as adaptability and versatility as one charts a career path?