Try this method, one of many...
The independent sharp subject layer above the blurred layer keeps the edges intact, In conclusion you can independently adjust the subject and/or background for exposure, color, filtering, etc. And, adding a layer mask to each layer will provide even greater control.
1.) Isolate the subject on the new layer as precisely as possible with whatever selection technique works best for you.
2.) use Ctrl J placing the SELECTED area/subject onto a transparent bkgd.
3.) Ctrl click the new subject layer thumbnail to re-activate selection, click on the original background layer, and then Ctrl Shift I to invert the selection.
4.) Ctrl J again to place the background w/o subject onto a transparent layer. Note -you want the subject layer w/transparent bkgd to be above the background w/o subject layer in the layers palette.
5.) Apply the blur to background w/o subject layer
6) If necessary go around the boundaries at a very high magnification and modify the edge with a tiny, lowered opacity soft edge eraser.
Best,
Chas