Final answer:
Wigs are the hairpieces with openings in the base through which the client's own hair can be blended.
Step-by-step explanation:
The hairpieces with openings in the base through which the client's own hair can be blended are called wigs. Wigs are a popular choice for people who want to change their hairstyle or cover up hair loss. They are available in various styles, lengths, and colors and can be easily blended with the client's natural hair for a realistic look.