Cheap, plastic, ball-point pens can be pretty nasty in the right hands. If you know where to stab someone for maximum effect, you can kill with one. The cylindrical structure will stay ridged, so you can drive it in with a shocking amount of force.
Being able to use improvised weapons like this is very dependent on your practical understanding of human anatomy. If you know exactly where poking a hole in someone will do horrific things, it’s an option. Otherwise, you’re better off just reaching for a letter opener, or a heavier ink pen.
It’s probably worth noting that tactical pens are a real thing. These are a viable self defense tool and can really mess someone up. Though, again, the expectation is that you know where to put it for maximum effect. The differences from a normal pen is the heavier construction, (usually titanium, though I’ve seen aircraft aluminum and stainless steel advertised). These sometimes also feature sharpened edges, false tips, and extended non-slip grips to allow for easier use as an emergency weapon.