This was a soft body test for hair.
The hair is deformed with a mesh deform modifier, the deform cage has soft body physics enabled.
I had problem with the mesh deform cage.
The top / first set of vertices were lagging or moving preemptively.
I found it was the Cache Steps property, I set it to 2, and it worked correctly.
If you set Cache Steps to 20, then bake, you may see the first set of vertices lag behind the hair.
I had the same problem in the project file, though the cage vertices were moving preemptively.
soft_hair.blend (465 KB)