Get soft body to retain shape after collision?

See the picture I have attached. What I’d like to do is have the soft body pillow retain the imprint of the sphere, after it collides. Currently, the sphere collides with the pillow, it jiggles a bit, and then goes back to its original shape. Is there a way to keep the imprint for the rest of the animation? Note – I don’t want to convert the animation to mesh – I’d rather do it all with the physics simulations if possible. Thanks in advance!

I don’t want to convert the animation to mesh
If you just want to create a mesh from a particular frame bake the soft body simulation and just apply the soft body modifier when on that frame that has the object shape you want.

Is there any way to get the object to behave more like a pillow in general? Be less bouncy, and more shock-absorbant?

Play with the Soft Body Edge parameters, like Pull, Push and Damp.