Finally, a part of the horribilis Dei maiestas is that God has not chosen everyone for salvation but has left others to perish in their original and actual sin. We usually call the manifestation of God’s justice “reprobation” or “double predestination.” Reprobation is as equally ultimate in the decree of God as election. We see this in Scripture. God “hardens whomever He wills” (Romans 9.18) and “make[s] out of the same lump one vessel for honored use and another for dishonorable use” (Romans 9.21). Those made for dishonorable use God “has prepared for destruction” (Romans 9.22). They are described by Peter in these terms: “They [unbelievers] stumble because they disobey the word, as they were destined to do” (1 Peter 2.8). Jude uses these words: “For certain people have crept in unnoticed who, long ago, were designated for this condemnation” (Jude 4).
This destruction and condemnation cannot be imputed, attributed, or blamed on God. The basis on which God manifests His justice in leaving or passing by those He does not elect in mercy is their sin and unbelief. Again, the Canons of Dort later explained what was implicit in the Belgic [Confession]:
What peculiarly tends to illustrate and recommend to us the eternal and unmerited grace of election is the express testimony of sacred Scripture that not all, but some only, are elected, while others are passed by in the eternal decree, whom God, out of His sovereign, most just, irreprehensible, and unchangeable good pleasure, has decreed to leave in the common misery into which they have willfully plunged themselves, and not to bestow upon them saving faith and the grace of conversion but, permitting them, in His just judgment, to follow their own ways, at last, for the declaration of His justice, to condemn and punish them forever, not only on account of their unbelief, but also for all their other sins. And this is the decree of reprobation, which by no means makes God the author of sin (the very thought of which is blasphemy) but declares Him to be an awful, irrprehensible, and righteous judge and avenger thereof (1.15).
From: With Heart and Mouth: An Exposition of the Belgic Confession by Daniel R. Hyde (Grandville: Reformed Fellowship, Inc., 2008), pp. 217-218.