Haj of old persons
Hadrat K’ab bin Marrah narrates that the holy prophetﷺ(sallallaahu alaihi wasallam) said: “If a person reaches his oldage in Islam, that would be the reason for his noor (light).” (Tirmizi, Nisayee)
Islam is such a holy Deen that has provided so many comforts for the old men in every sector and honoring them has been regarded as an obligatory as if the honor of Allah, as has been stated by our holy and beloved  prophetﷺ (sallallaahu alaihi wasallam):  “Honoring a Muslim old man is like disclosing the glory and  magnificence of Allah”.  (Abu Dawood, Baihaqi)
By the way there are different and easy commandments in the affairs of Hajj for old persons.
Special commands with regard to the Hajj for old persons
If someone’s parents are old enough to perform Hajj and its rituals with much strain the difficulty (but Hajj has become obligatory on them), then their progeny could perform Hajj and Umrah on their behalf.
In the same way, if anyone has become so old that he could not ride on a vehicle and go to perform Hajj or Umrah, it is imperative on his part to nominate a representative on his behalf to perform Hajj or Umrah.  That would be enough for him till such time that even if he becomes able to ride the vehicle and perform Hajj or Umrah while the nominated person had worn Ihram for Hajj on his behalf.  Then too, Hajj performed on his behalf would become accepted.
It has been narrated by Abdullah bin Abbas RadhiAllahuta’la anhu that “A lady from Qash’am clans asked the holy prophet ﷺsaying:  Hajj has become obligatory on the part of my father but he is very old and could not properly sit on the back of the camel, hence can I perform Hajj on his behalf ?”  the holy prophet ﷺ said: “yes! You can perform Hajj on his behalf.  (Sahih Bukhari Hadith 1854)
If the Hajj was not obligatory on the part of the parents, then on their behalf Hajj could not be performed.  However, the Hajj was obligatory on the part of the parents but they expired then Hajj could be performed on their behalf, not Umrah. Moreover, such proxy Hajj could be performed by the one who has already performed a Hajj.
For a person who has been nominated to perform a Hajj, he has to fulfill two conditions:
Firstly, he is qualified in all respect for performing a Hajj, and secondly, he should have already performed a Hajj.  If he has not performed Hajj prior to undertaking for another person, then this Hajj could be regard as a Hajj from his side and not for whom he agreed to perform. It has been narrated by Abdullah bin Abbas RadhiAllahuta’la anhu that “the holy prophet ﷺ  heard a person saying Labbaik ‘An Shabarmah and asked: who is Shabarmah?  The person said “my brother or a relative”, then the holy prophetﷺ asked him if he himself had performed Hajj earlier, he said ‘no’,  then the holy prophetﷺ  said: Perform a Hajj for you first and then perform on behalf of Shabarmah.”  [This hadith has been narrated by Imam Abu Dawood].