It sounds like we're on the same page. Basically, I'd love the ability to cut a tapered stroke and have the option to not have it change it's remaining shape automatically. So if I had a stroke width selected that featured a taper at both ends, after I lay the stroke down, I could use the erase to cut it in the middle and the two resulting smaller strokes would then only have one end each still tapered and the other would be thick with a flat edge resulting from the cut.
If you're getting another cool idea that is not what I'm suggesting that is all good! But For sake of clarity I made a diagram to show what I meant:
Diagram 1 - shows how the tapered stroke reacts after being cut - this is not bad - but would love the next option I show as well.
Diagram 2 - the black circle shape is the initial stroke - the green stroke over top is the new crossover stroke. If I cut that stroke with the pencil eraser option, the red line shows what happens - it tapers at both ends adjusting to the new size. The purple line shows the alternative option for cutting that I would like to see. where both ends retain the original taper width effect where cut.
At the risk of beating a dead horse - I wanted to be sure I was clear in the first diagram - in the pic below - you see the dual tapered stroke - then part 2, shows after it's cut in two pieces, the line adjusts automatically - the third part shows the option I'd like to see