Did that snap off during use, all of a sudden? If so, I'm not sure how that could happen but if you are messing around with the filament and it bends enough, it will get weak. It doesn't take much to snap it off.

However, when it does happen what I do that works well is to take the tip of an xacto knife blade and put it in the center of that snapped off stub. I spin it slowly and drill a comical shaped hole in the end just deep enough so that you can see it's there. If you go too deep you'll carve out the side. Then I sharpen the end of the new piece of filament coming in, feed that through the extruder feeder and place that sharp tip into the conical hole. That keeps the new filament from slipping off. Then once the head is heated hold that joint and feed about 20mm of filament with the slicer and it pushes the new filament in. It works really well for me.

What this technique does that I like is keep me from moving or messing up my tolerances. If you push that filament in by hand you'll tend to push down on the entire hotend carrier and if you push enough, you'll make something change and might cause you to have to recalibrate the 1st layer gap unnecessarily.