Blood vessels that have thinner walls that are more likely to collapse when blood is withdrawn during a venipuncture are called:

Blood vessels that have thinner walls that are more likely to collapse when blood is withdrawn during a venipuncture are called veins.

Differently form arteries, veins are blood vessels with thin, less muscular walls. Veins have thinner walls because the blood pressure in them is much lower.

So, as a result of common intravenous injections (such as venipuncture), collapsed veins might occur. Veins are then temporarily blocked.

The answer is; veins

Smaller veins are prone to collapsing during venipuncture than larger veins. Due to the suction force created by the needle syringe, the higher outer pressure may cause the walls of the veins to collapse. Once collapsed, the inflamed walls are hard to recover. This stops the flow of blood through the veins. However, the body forms new smaller veins.