I got something like this from a co-worker:
I can no longer keep up with things here. I just don't know how to approach tasks and I also have now clue how to catch up with things here.
To me, this really sounds like "inner resignation" and I already told my boss about that, but nothing happend yet.
Till now, I was giving him advice and assigned tasks to him that are important for us right now, but his performance continues to be inferior compared to other co-workers.
On the other hand, I don't think my co-worker is totally aware of his (serious) situation.
How can I help my coworker improve?
Just do nothing is perfectly viable for me at this point, as my boss is aware of this.
Talk to my coworker and ask him, what he wants to do in the future? I.e. making him aware that he already resigned sort of.
Continue to support him by mentoring, providing ideas and guidelines.
Getting HR involved. And then bad things will happen.
Some additional information:
I'm just a co-worker that knows some details.
He is a peer, but a junior from a technical pov.
I won't involve HR.