I agree that you'll never get your money back from a piece of jewelry, but the useful-value can be tremendous.
I'm the fourth generation to own this lovely stone, and I'm certainly not "wearing it out". As I said, I intend this ring to one day go to my only grandson, and by then he may choose to have it re-set, but the stone will still be just as lovely as the day Pappy Lloyd gave it to Great-Grandmother Mary.
I think you're referring to an old-fashioned cut called the "Old Mine Cut", so named because the raw diamonds were taken from old-old mines that had been producing for a long time /not newer locations. It's a vintage diamond -- probably from the 1700s-1800s that was cut by hand (before machines). It's also called a Pillow Cut because it's slightly rectangular in shape. Stones of this era were prepared with fewer cuts than today's most popular "Brilliant Cut", and they were designed to look their best /sparkle in candlelight.
My great-grandmother's ring is an "Old European Cut", which is what followed the "Old Mine Cut". It is also hand-cut with fewer faucets, but it is round rather than that "soft rectangle shape".