It is allowed to perform Hajj on behalf of someone who did not do so provided someone performed Hajj themselves.
The proof:
عَنِ ابْنِ عَبَّاسٍ، أَنَّ النَّبِيَّ صلى الله عليه وسلم سَمِعَ رَجُلاً يَقُولُ لَبَّيْكَ عَنْ شُبْرُمَةَ . قَالَ ” مَنْ شُبْرُمَةَ ” . قَالَ أَخٌ لِي أَوْ قَرِيبٌ لِي . قَالَ ” حَجَجْتَ عَنْ نَفْسِكَ ” . قَالَ لاَ . قَالَ ” حُجَّ عَنْ نَفْسِكَ ثُمَّ حُجَّ عَنْ شُبْرُمَةَ
Narrated Abdullah ibn Abbas (may Allah be pleased with him):
The Prophet (ﷺ) heard a man say: Labbayk (always ready to obey) on behalf of Shubrumah. He asked: Who is Shubrumah? He replied: A brother or relative of mine. He asked: Have you performed hajj on your own behalf? He said: No. He said: perform hajj on your own behalf, then perform it on behalf of Shubrumah
[Saheeh Sunan Abi Dawood no. 1811]
Hafidh Ibn ‘Abdul-Barr rahimahullah said:
“And in this Hadith is also evidence for the permissibility of a man making Hajj for another person”
[Tamheed (9/134)]
He also said: “Malik said: It is allowed to make Hajj for a deceased who did not make Hajj himself. However, it is preferred that he perform Hajj himself first. This is the statement of Abu Haneefah, ath-Thawri, and al-‘Awzaai’. al-Hasan as-Saalih said: He does not make Hajj for himself except the one who made Hajj himself”
[Tamheed (9/136)]
And Allah Knows Best
Faisal Ibn Abdul Qaadir Ibn Hassan
Abu Sulaymaan