Putting a UICorner inside a frame is supposed to disable BorderSizePixel, as the engine will not let you set it.
However, it appears that if a Frame gets too small to be rounded, it will begin rendering the border. This is common for dynamically resized frames in BillboardGuis.
Here is what happens when our Stamina bar depletes, notice the Border re-appears:
Expected behavior
It should never render the border if there is a UICorner