When you use a dispenser to put a chest plate on a pillager, the pillager will wear it but the chest part of the texture appears under them and below the feet. The shoulder texture is correct though. The pillager was spawned in using a spawn egg and this was found in an "old" type world.

Steps to reproduce:
1. Spawn Pillager
2. Put a dispenser facing the pillager
3. Put a chest plate of any type in
4. Activate dispenser