I remember with great displeasure the bad old days of creating a 3x3 table for every container and jamming a rounded corner gif into each of the four corners to create this effect.
I dunno, I look back on the <table>-based layout days with fondness, probably because I was young and the Web was nothing but rolling green fields and endless potential. I didn't see the limitations, only the opportunities for inventiveness. I'll never feel the same satisfaction as I did when those first few website designs came together.
In games you had to do this 9 piece slice, one slice for each of the 4 corners, all 4 straight sides that can be repeated as a pattern and the middle background piece
Nine-patch image scaling[0] is still a thing, and is only orthogonally related to setting a border radius (it's a hell of lot more versatile than that).