Using V2019, a monitor with good resolution: MultiSync EA244WMi @1920 x 1200, NVidia GTX 1050 Ti driver, I cannot replicate this behavior.
I drew 3 lines with widths of : 0.25 pt, 0.125 pt, and 0 pt.
There is a zoom a zoom out threshold where all of the lines appear to have the same visual thickness. But, all lines remain visible until the image is so small I can barely see it.
When I zoom in, below the threshold, then various widths become distinguishable. The 0.25pt and 0.125pt lines hit their designated thicknesses and do not change after that. The 0 pt line just continues to shrink.
Saving as PDF has a different behavior. The 0 pt line is set to some default size. Zooming out does not cause the lines to disappear. There is some threshold beyond which all lines have same visual thickness. Below that, the 0 pt line is always the heaviest of these three.
Anyway, these are my observations. Within Visio, I imagine both the display, display settings, and driver have a strong impact. Going to PDF changes this dynamic.