Common names can change from county to county, so without a picture, Latin name or description it's hard to say.
It's possible the common name intended was Live Forever rather than Never Die. There is a Sedum or Showy Stonecrop that goes by that common name. Google it for a photo & see if that's your plant.
Thats it......Sedum........so, here are my questions.......how and when to split/transplant........and, my buds are not blooming, instead they are browning and dying...........what stimulates them to bloom........could I have caused this by applying Diazinon in my yard and killing off bugs?
Quite possibly, that stuff is pretty deadly. You haven't said how much sun the area gets, what the soil is like or how often they get watered, all of which could matter too.
i wasn't aware of the "deadly" properties that the plant has.....I grow it both in sunny and shady areas with adequete drainage.......l seldom water it, it seems to do well on its own.......
I've grown Sedum both in the shade and sun. The one in the shade needs very little water and does fine. The one in the sun, I water along with the other plants in that garden. I don't know that it needs the water, it never seems to wilt, but it certainly doesn't mind it. The only time I've seen one die, is if it's crowded out and shaded by other plants (in my case, Hosta). It slowly dissappeared. As for yours not having flowers, it might be that the summer sun in the south (this year) is too much for the buds. It has been exceptionally hot. Try moving it to a part shade location. Most plants transplant (and split) best in the spring or fall, but with Sedum.... it's pretty tough, you could try moving it now and it will probably do OK. I've had animals dig them up and I've found them laying on the dirt... stuck them back in, watered, and they did fine. They are hard to kill. :)
... hence the name Live Forever or Never Die! I think Rima meant that Diazinon is pretty deadly, not that the sedum is.