'Broken off' in the Bible

“My days are past, my purposes and plans are frustrated and torn apart;The wishes of my heart [are broken].

When its branches are dry, they are broken off;The women come and make a fire with them.For they are not a people of understanding,Therefore He who made them will not have compassion on them,And He who created them will not be gracious to them.

In fierce anger He has cut off and destroyedEvery horn of Israel.He has withdrawn His right handFrom the presence of the enemy.And He has burned in Jacob like a flaming fireConsuming all around.

‘But the vine was uprooted in [godly] wrath [by His representative]And it was thrown down to the ground;The east wind dried up its fruit.Its strong branch was broken offSo that it withered;The fire [of God’s judgment] consumed it.

If anyone does not remain in Me, he is thrown out like a [broken off] branch, and withers and dies; and they gather such branches and throw them into the fire, and they are burned.

But if some of the branches were broken off, and you [Gentiles], being like a wild olive shoot, were grafted in among them to share with them the rich root of the olive tree,