1/ It seems possible to stop evolution !
There are lots of examples of earthlings species which evolution has stopped at a certain point, for example this bacteria living in the deep ocean has not changed since 2 billions years.
Add crocodiles, trilobites and other species. They found a place in nature that fits them so perfectly they (quite) stopped their evolution.
You could imagine a specie that stop evolving while finding the perfect balance, like my very old bacteria.
2/ Except it is not possible.
In fact, some species did evolve from these, but the original specie was not extincted as the new one did not replace them. These species seems freezed in evolution, but if they are so perfect, why don't they rule the world ?
They have a very specific place and climate they are adapted to. They don't spread worldwide. If they become too numerous, they die (from hunger and lack of vital resources).
I'm not sure how a unique plant could evolve and how climate could be the same everywhere, but let's assume that the case, you have the same plant everywhere, and the climate is... perfectly perfect. The plant grows. And grows. 671
It spreads worldwide. Wow.
If nothing threatens your plant, then nothing stop it from growing. Your plant become its own ennemy : the nutrient the plant needs to grow will lack. The shadow from the grown-up plants will hide the sun from the youngs. Or, if it's perfectly flat, the place will lack for the youngs and nothing will replace an old dying plant on a ground without the essential nutrients (as the old plant has already deeply used it to grow)
As a result, the young plants will die, except the ones with a small mutation allowing them to accept another kind of nutrient, or less sunlight, or growing above the other. A new specie is born. Evolution strikes agains.
You could argue that the young plants can live from the dead old plants (That sounds creepy) but on earth, a lot of other species are needed to decompose a plant (worms, bacterias...). If the plant can "eat" herself still living or not decomposed, it will have a serious bad time with its "child", but that could be the one and only way your unique plant could rule the world, all alone.
And even with that solution, I'm not sure it's not already a new specie, as the first generation eats from the ground and the new generation eats froms the old plants, and might develop another way to absord nutrients. 731