He entered ihram for Hajj but he did not stipulate a condition (that if he was prevented from completing it, he would exit ihram at the point at which he was prevented from continuing), then he missed the standing in ‘Arafah (whether because of illness or being delayed or without any excuse). What does he have to do, and how can he exit from his ihram?

Praise
be to Allah.

Firstly: 

Standing in ‘Arafah is one of the pillars
or essential parts of the Hajj; in fact it is the major pillar, because the
Messenger (blessings and peace of Allah be upon him) said: “Hajj is ‘Arafah;
whoever comes [to ‘Arafah] on the night of ‘Arafah, before dawn breaks on
the night of Jam‘ [Muzdalifah] has completed his Hajj.” Narrated by at-Tirmidhi
(889) and an-Nasaa’i (3016). Classed as saheeh by Shaykh al-Albaani (may
Allah have mercy on him) in Saheeh an-Nasaa’i. Whoever does not come
to ‘Arafah before dawn breaks on the Day of Sacrifice, even for a moment or
passing through, has missed out on Hajj, according to scholarly consensus. 

An-Nawawi (may Allah have mercy on him)
said in al-Majmoo‘ (8/273): If he enters ihram for Hajj, but does not
stand in ‘Arafah until dawn breaks on the Day of Sacrifice, he has missed
out on Hajj, according to scholarly consensus. End quote. 

Secondly: 

The one who misses out on Hajj – and had
not stipulated a condition when first entering ihram, that his exiting ihram
would be at the point where he was prevented from continuing – must do a
number of things: 

1.    
He must exit his ihram by
doing ‘umrah

2.    
He must make it up the
following year, even if the missed Hajj was voluntary.

3.    
He must offer a sacrifice as
well as making it up.

4.    
He must repent if there was
no excuse for his delay. 

This is a summary of what the one who
misses Hajj must do. 

Explanation of these points with evidence
is as follows: 

1.    
The one who missed out on
Hajj must exit his ihram by doing tawaaf and sa‘i, and cutting his hair or
shaving his head (‘umrah) 

That is because of the report narrated by
Maalik in al-Muwatta’ (870), that Abu Ayyoob al-Ansaari (may Allah be
pleased with him) set out for Hajj, then when he was in an-Naaziyah, on the
way to Makkah, he lost his mount. He came to ‘Umar ibn al-Khattaab (may
Allah be pleased with him) on the Day of Sacrifice and told him what had
happened. ‘Umar said: Do what those who do ‘Umrah do, then you will have
exited your ihram. Then when Hajj comes next year, do Hajj and offer
whatever sacrificial animal you can afford. Its isnaad was classed as saheeh
by an-Nawawi (may Allah have mercy on him).

See: al-Muntaqa Sharh al-Muwatta’
(3/7); al-Majmoo‘ (8/274) 

2.    
 With regard to its being
obligatory to make up that Hajj and offer a hadiy (sacrificial animal) 

that is because of the report narrated by
‘Ikrimah, who said: I heard al-Hajjaaj ibn ‘Amr al-Ansaari say: The
Messenger of Allah (blessings and peace of Allah be upon him) said: “Whoever
breaks a bone or becomes lame has exited ihram, but he must do Hajj the
following year.” ‘Ikrimah said: I asked Ibn ‘Abbaas and Abu Hurayrah about
that and they said: He is telling the truth. Narrated by Abu Dawood (1862).
According to another version: “Whoever breaks a bone or becomes lame or
falls sick.” Classed as saheeh by al-Albaani in Saheeh Abi Dawood

That is also because of what ‘Umar said to
Abu Ayyoob al-Ansaari (may Allah be pleased with them both): “Then when Hajj
comes next year, do Hajj and offer whatever sacrificial animal you can
afford.” 

This is the view of the Hanafis, Maalik,
ash-Shaafa‘i and the Hanbalis. 

Maalik narrated from Naafi‘, from
Sulaymaan ibn Yasaar, that Habbaar ibn al-Aswad came on the Day of Sacrifice
when ‘Umar ibn al-Khattaab was offering his sacrifice, and said: O Ameer al-Mu’mineen,
we miscounted the days and we thought that today was the day of ‘Arafah.
‘Umar said: Go to Makkah and do tawaaf (and sa‘i), you and the people with
you, and slaughter the sacrificial animal, if you have one, then shave your
head or cut your hair, and go home. Then next year, do Hajj and offer the
sacrifice; whoever cannot afford it, let him fast three days during Hajj and
seven days after he has returned home. 

See al-Majmoo‘ (8/275) 

Ibn Qudaamah said in al-Mughni
(3/280):

The sacrifice is required of the one who
misses Hajj, according to the more correct of the two reports. This is the
view of those whom we have named among the Sahaabah and fuqaha’, apart from
ashaab ar-ra’y, who said that he does not have to offer a sacrifice. In
support of our view, we have the hadith of ‘Ata’ and the consensus of the
Sahaabah. End quote. 

He also said (3/281):

If he has brought a hadiy (sacrificial
animal) with him, he should sacrifice it [i.e., in the year in which he
missed Hajj], that does not take the place of the sacrifice he has to offer
in the following year. Rather in the following year he must also bring a
hadiy. This was stated by Ahmad. That is because of the hadith of ‘Umar (may
Allah be pleased with him). End quote. 

See also al-Majmoo‘ (8/275) 

3.    
In the rulings mentioned
above there is no differentiation between the one who has a legitimate
excuse and the one who does not, but there is a difference between them in
terms of sin; the one who has an excuse is not sinning, whereas the one who
has no excuse is sinning. This was clearly stated by al-Qaadi Abu’t-Tayyib
and others. See al-Majmoo‘ (8/276) 

And Allah knows best.