Final answer:
The false statement about a Product Family after deployment is that it can be renamed; this is usually avoided to prevent market confusion and branding issues, while other modifications such as removal, addition of product lines, and models are common.
Step-by-step explanation:
The statement that is false about a Product Family after it is deployed is: C. The Product Family can be renamed. Once a product family has been deployed in the market, renaming it can cause confusion and may lead to branding and marketing challenges. Therefore, while it is technically possible to rename a product family, it is usually not done due to the potential negative consequences.
In contrast, the Product Family can indeed be removed (A), although this would likely be a business decision based on factors such as market performance or strategic shifts. Product lines can certainly be added to the Product Family (B), enabling a business to expand its offerings and address additional market segments. Lastly, the Product Family can have Models added to its Product Lines (D), which is a commonplace practice for updating and refreshing a product line to keep it competitive and relevant.