During the last day of Mahabharata war, Kripa accompanied Aswathamaa and helped him to execute the bloody murder of the Upapandavas and other soldiers in Pandava Army. After which there is no mention about Kripacharya in Mahabharata. What happened to him after that? The immortality conferred on him (It is well known that he is Chiranjeevi) is a blessings or curse like Aswathmaa?
Kripacharya was blessed with longetivity till the end of the Kalpa (Chiranjeevi) and also is scheduled to become one of the Saptarishis of the next Manvantara, as I discuss in this answer.
Also, after the Mahabharata war, as discussed in this answer:
Kripa was installed as the preceptor and Parikshit was made over to him as his disciple.
But, after the decline of the Kuru dynasty, at the advent of Kaliyuga, he must have resorted to his Ashrama, as evident from this verse from the Śrīmad-Bhāgavatam Purāṇa:
गालवो दीप्तिमान्रामो द्रोणपुत्र: कृपस्तथा ।
ऋष्यशृङ्ग: पितास्माकं भगवान्बादरायण: ॥ १५ ॥
इमे सप्तर्षयस्तत्र भविष्यन्ति स्वयोगत: ।
इदानीमासते राजन् स्वे स्व आश्रममण्डले ॥ १६ ॥
O King, during the eighth manvantara, the great personalities Gālava, Dīptimān, Paraśurāma, Aśvatthāmā, Kṛpācārya, Ṛṣyaśṛṅga and our father, Vyāsadeva, the incarnation of Nārāyaṇa, will be the seven sages. For the present, they are all residing in their respective āśramas.
Thus, as per Śrīmad-Bhāgavatam, currently, Kripacharya is residing in his Ashrama (but I don't know where the ashrama might be) and will become a Saptarishi in the next Manvantara.
When Pandavas had decided to renounce the world, Kripacharya was installed as the preceptor of Parikshit. This incident is mentioned in Mahabharata, Book 17: Mahaprasthanika Parva, Section-1.
"Having said these words, king Yudhishthira the just, along with his brothers, promptly offered oblations of water unto Vasudeva of great intelligence, as also unto his old maternal uncle and Rama and others. He then duly performed the Sraddhas of all those deceased kinsmen of his. The king, in honour of Hari and naming him repeatedly, fed the Island-born Vyasa, and Narada, and Markandeya possessed of wealth of penances, and Yajnavalkya of Bharadwaja’s race, with many delicious viands. In honour of Krishna, he also gave away many jewels and gems, and robes and clothes, and villages, and horses and cars, and female slaves by hundreds and thousands unto foremost of Brahmanas. Summoning the citizens. Kripa was installed as the preceptor and Parikshit was made over to him as his disciple, O chief of Bharata’s race.
According to the Puranic Encyclopedia, Kṛpa died at the end like everyone else:
8). End of Kṛpa. The great war ended. Duryodhana and others were killed and, when Dhṛtarāṣṭra left for the forest with Gāndhārī, Kṛpa desired to accompany them. But, Dhṛtarāṣṭra did not permit it. as advised by Dhṛtarāṣṭra, put up Kṛpa with him. (Āśramavāsika Parva, Chapter 16, Verse 5). Before the Pāṇḍavas set out on their great journey Yudhiṣṭhira appointed Kṛpa as the preceptor of Parīkṣit, the son of Arjuna. (Mahāprasthāna Parva, Chapter 1, Verse 4). During his last days Kṛpa went into the forest for penance and there he breathed his last. (Śānti Parva, Chapter 296, Verse 14).
But I cannot find the verse in the latest BORI critical edition of the Mahābhārata so it's possible that over the centuries Kṛpa is made immortal a.k.a chiranjīvi by the various interpolators of the Mahābhārata.