Been noodling over this one most of the day. The commercial plastic eraser holders use a ratcheted slider that fits into a groove molded in the side of the barrel. The toothed arrangement on the groove/slider makes it possible to adjust the position of the eraser in the barrel of the holder.
How to do that in wood?????
The barrel needs to be 1/4" ID (and perhaps a bit smaller - perhaps a D bit) so that friction helps hold the the eraser in the barrel.
One thought is to design the end of the barrel as a collet - after turning the barrel, chase threads on the outside, and then put a saw kerf from the end to a point about 1/2 - 3/4" inch back. Then, turn a second piece, and chase matching threads on the inside, so that when it is screwed onto the threaded end of the barrel, it tries to compress the barrel along the saw kerf, which then grips the eraser. The problem (in addition to actually executing it) would be to keep it from becoming too bulky.