Modifying a selection (e.g. "Border") causes feathering

I tried to duplicate your issue as I have never heard of this happening and was unable. Please share your PS version and OS.

thanks,

The origin of the Select>Modify>Border or Select>Fringe as it was known in the first couple of photoshop versions was mainly used for blending pasted or floating selections into the content below. In the first several versions of photoshop 1, 2 and 2.5 there were no layers.

The selection made with Selection>Modify>Border is intended to be feathered.

One could select the edges of a floating selection with Fringe which as you have seen put a sort of feathered border around the existing selection and apply blurring with say Gaussian Blur to better blend in the floating selection with the content below before Defloat which made the content merge down into the area below.

Of course there are numerous creative uses for Select>Modify>Border including making some pretty interesting frames combined with layer styles.

Anyway, you could make your selection with the Rectangular Marquee Tool or Ctrl/Cmd click on the object layer, click on the Quick Mask Mode icon at the bottom of the toolbox and then go to Filter>Other>Maximum and enter the desired size of the stroke.

Then Exit Quick Mask Mode, which leaves a selection and go to Edit>Stroke and use Inside and enter the same amount you used in the Minimum filter.

1. Make selection of object such as Ctrl/Cmd clicking on the layer thumbnail in the layers panel

2. Click the Quickmask icon second from the bottom in the Tool Box, go to Filter>Other>Maximum and

    enter the desired border size. 16 in this example

3. Click on the Quickmask icon to exit and your left with a selection. Go to Edit>Stroke and for the amount

    use the same number as used in the Maximum filter then Inside for the Location