The stem won't take any stretch because it's accurately sized and there's no room for anything larger than what it was designed.

However, to my knowledge All bars have a bulge or sleeve in the center, including, I'm almost certain the one you removed. This is necessary partly to increase strength, but mainly because to provide added clearance to slip the bar through until you got to the clamping area.

For certain, your stem clamp diameter is larger than 7/8", though it's possible that you bought a replacement with the wrong (larger) clamp diameter than the original. Common clamp diameters are 1" (25.4mm) 26mm, 1-1/4" (31.8mm).

Measure the clamp diameter of your original bar, compare that to the replacement, and if they're different, buy a new bar that matches your old one.