2 Timothy 2:13 If we believe not, yet he abideth faithful: he cannot deny himself.
"If a man abide not in me, he is cast forth as a branch, and is withered; and men gather them, and cast them into the fire, and they are burned."
The same as the Old Covenant, God remains faithful to His promises, both positive and negative. When God abides faithful, it reminds us that when some people do not abide in Him, "It is a terrifying thing to fall into the hands of the living God." (Heb. 10:31.) God cannot deny His own standards, He remains faithful to them.
When someone has died, it is common for people to ask... "Did they go to heaven?" Especially when they were not overt Christians. I cannot claim to be God and know their hearts. My answer is usually, "I do not know where they are, but one thing I do know is, they are in the hands of a Just God." Now the question comes to mind, does the thought of being in the hands of a Just God strike terror in you? Or does it comfort you?
The verse immediately before this gives the context of it all, "If we endure we shall also reign with Him; If we deny Him, He also will deny us;" Yet, He abides faithful to do this. Don't doubt God.
The problem here is that believers are not seeing those who get cut off and left behind are still saved. Those left behind is where the vessels unto dishonor comes from that are still in His House that did not depart from iniquity. Those who do, shall be received as vessels unto honor in His House. Those who do not by the time the Bridegroom comes, will be disqualified as in reprobate from attending the Marriage Supper of the Lamb in Heaven.
So any unrepentant iniquity is the same as denying Him verbally but by their works;
Titus 1:16 They profess that they know God; but in works they deny him, being abominable, and disobedient, and unto every good work reprobate.
Paul gives an example of a former believer where he errs from the truth and had his faith overthrown but he says "nevertheless" in pointing out again of 2 Timothy 2:13, that the foundation of God stands sure with His seal for why former believers are still to be called to depart from iniquity so they can be that vessel unto honor in His House as received by the Bridegroom when He comes.
2 Timothy 2:18 Who concerning the truth have erred, saying that the resurrection is past already; and overthrow the faith of some. 19 Nevertheless the foundation of God standeth sure, having this seal, The Lord knoweth them that are his. And, let every one that nameth the name of Christ depart from iniquity. 20 But in a great house there are not only vessels of gold and of silver, but also of wood and of earth; and some to honour, and some to dishonour. 21 If a man therefore purge himself from these, he shall be a vessel unto honour, sanctified, and meet for the master's use, and prepared unto every good work.
So if a believer depart from iniquity, he purges himself by His grace & by His help ( Hebrews 12:1-2 & 2 Timothy 4:18 ) to be received as that vessel unto honor and yet those who do not repent, that foundation still remains along with that seal of adoption, but disqualified to be resurrected after the great tribulation as vessels unto dishonor in His House for why there are vessels of dishonor in His House that did not depart from iniquity. They will weep and gnash their teeth over the loss of that firstfruit of the resurrection, and they will get stripes per the knowledge for not being ready, but He still calls them servants just as the prodigal son gave up his inheritance for wild living but he is still son.