reprobation
The sovereign decision of God before creation to pass over some persons, deciding not to save them, and to punish them for their sins and thereby to manifest his justice.1

• From scripture

The Lord has made everything for its purpose,

even the wicked for the day of trouble. (Proverbs 16:4 ESV)

For certain people have crept in unnoticed who long ago were designated for this condemnation, ungodly people, who pervert the grace of our God into sensuality and deny our only Master and Lord, Jesus Christ. (Jude 1:4 ESV)

• From The Canons of Dordt, First Main Point of Doctrine: Divine Election and Reprobation: 

Article 15: Reprobation

Moreover, Holy Scripture most especially highlights this eternal and undeserved grace of our election and brings it out more clearly for us, in that it further bears witness that not all people have been chosen but that some have not been chosen or have been passed by in God’s eternal election—those, that is, concerning whom God, on the basis of his entirely free, most just, irreproachable, and unchangeable good pleasure, made the following decree:

to leave them in the common misery into which, by their own fault, they have plunged themselves; not to grant them saving faith and the grace of conversion; but finally to condemn and eternally punish those who have been left in their own ways and under God’s just judgment, not only for their unbelief but also for all their other sins, in order to display his justice.

And this is the decree of reprobation, which does not at all make God the author of sin (a blasphemous thought!) but rather its fearful, irreproachable, just judge and avenger.

• From Systematic Theology by Wayne Grudem:

[W]e must be careful of our attitude toward God and toward these passages of scripture [that teach reprobation]. We must never begin to wish that the Bible was written in another way, or that it did not contain these verses. …[W]e are obligated both to believe it and accept it as fair and just of God…. In this context it may surprise us to see that Jesus can thank God both for hiding the knowledge of salvation from some and for revealing it to others: “Jesus declared, ‘I thank you, Father, for such was your gracious will’” (Matt. 11:25-26).

Moreover, we must recognize that somehow in God’s wisdom, the fact of reprobation and the eternal condemnation of some will show God’s justice and also result in his glory. Paul says, “What if God, desiring to show his wrath and to make known his power, has endured with much patience the vessels of Wrath prepared for destruction” (Rom. 9:22). Paul also notes that the fact of such punishment on the “vessels of wrath” serves to show the greatness of God’s mercy toward us. God does this “in order to make known the riches of his glory for the vessels of mercy” (Rom. 9:23).