  We prove that every complete metric space with property (Z) is a length
space. These answers questions posed by Garc\'{i}a-Lirola, Proch\'{a}zka and
Rueda Zoca, and by Becerra Guerrero, L\'{o}pez-P\'{e}rez and Rueda Zoca,
related to the structure of Lipschitz-free Banach spaces of metric spaces.
