The character’s flesh is soft and the object pressed against it is rigid, so the skin should deform a bit and the mesh should wrap around the mesh of the object.
I tried using soft body simulation and cloth simulation; neither gave me the expected result. (The character mesh deformed and looked to be vacuumed towards the object)
How exactly can I achieve the said result? Is there an important setting I’ve overlooked?
Quite basic setup ... works in some way ... but since you didn't provide any better description or details about your file (or result issue) ... there is not a way to help you ... sorry.
Note: Just because eye balls were hanging after the punch, I added a triangle face inside the head to connect eyes with back part oh the head.
Hard to really answer without a scene or more context, but the most common approach to this is to just add a shape key or post bake sculpt during the interaction and animate that, don't overcomplicate it. https://docs.blender.org/manual/en/latest/animation/shape_keys/index.html .
The technique in question is called "Shot Sculpting" in vfx.
I've worked with studios that do full body skin simulations for this and not only does it require a lot of manual tweaking it's computationally expensive. Fun to experiment with but be prepared for a lot of pain if you go this approach.
