There are only two things that can ruin a hardwood floor beyond all hope: floods and urine.
Floods are fairly rare, but almost everybody has dog or a cat that will eventually leave a oops on the hardwood floor.
If you catch the puddle and wipe it up while it’s still fresh, the problem is minimal; modern polyurethanes are designed to resist accidents like this.
But as urine sits and decomposes, it becomes more alkaline and more corrosive and eventually you have the equivalent of undiluted ammonia burning through your finish and into your wood. This tends to happen when there is carpet or a rug over the hardwood floors because it keeps the liquid from drying and allows it to sit in contact with the floor below as it breaks down.
The problem is compounded by the fact that pets, once they've marked a spot, continue to use it which practically guarantees that there will always be fresh ammonia forming at that site. Unfortunately, neither the wood finish nor the finish itself can resist this onslaught.
For some reason, there is a persistent belief that stains like these can be removed easily by sanding or bleach.
Unfortunately, this simply isn’t true. The vast majority of pet stains have to be patched out; that is, the damaged wood must be removed and replaced with new wood.
By the time a pet stain is as dark or extensive as the ones shown here, the ammonia burn has penetrated deeply into the hardwood, probably far deeper than you would want to sand. So don't waste your money on anything "guaranteed" to remove pet damage.