If he bought a car by instalments and dies, will he not be forgiven until it is paid off on his behalf?

Praise be to Allah.

Firstly: 

It is permissible to buy a car or any other item by instalments, even if that is for a price that is higher than the cash price. This has been explained previously in the answers to questions number 13973 and 104815 . 

Secondly: 

The instalments that you owe are regarded as being a debt that you owe. 

No one should incur debts except in the case of need, because of what is narrated in the texts of seeking refuge with Allah from debt and asking Allah to pay it off, and that one's soul is in pledge to this debt until it is paid off. Muslim (1886) narrated from ‘Abd-Allaah ibn Amr ibn al-‘Aas (may Allah be pleased with him) that the Messenger of Allah (blessings and peace of Allah be upon him) said: “The martyr will be forgiven for everything, except debt.” 

Al-Nawawi said in Sharh Muslim: As for the words of the Prophet (blessings and peace of Allah be upon him), “except debt”, this is drawing attention to all the rights of human beings, and indicates that jihad, martyrdom and other righteous deeds do not cause duties to human beings to be waived; rather they cause duties to Allah, may He be exalted, to be waived. End quote. 

Al-Nasaa’i (4605) narrated that Muhammad ibn Jahsh (may Allah be pleased with him) said: We were sitting with the Messenger of Allaah (peace and blessings of Allaah be upon him) when he raised his head towards the sky, then he put his palm on his forehead and said: “Subhaan-Allaah!  What a strict issue has been revealed to me!” We remained silent and were afraid. The following morning I asked him, “O Messenger of Allaah, what is this strict issue that has been revealed?” He said, “By the One in Whose hand is my soul, if a man were killed in battle for the sake of Allaah, then brought back to life, then killed and brought back to life again, then killed, and he owed a debt, he would not enter Paradise until his debt was paid off.” Classed as hasan by al-Albaani in Saheeh al-Nasaa’i, 4367.   

Ibn ‘Abd al-Barr said in al-Tamheed (23/238):  

The debt for which a person will be kept out of Paradise – and Allaah knows best – is that for which he left behind enough to pay it off but he did not leave instructions to that effect, or he was able to pay it off but did not do so, or he took the loan for some unlawful or extravagant matter and died without having paid it off.  

As for the one who took a loan for something lawful because he was poor, and he died without leaving behind anything to pay it off, Allaah will not keep him from Paradise because of it, in sha Allaah. End quote. 

If a person buys a car by instalments, in the event of his death it may be possible to pay off his debts or a large part of it from the price of the car after selling it. 

Hence we say: There is nothing wrong with you embarking upon this transaction so long as you are determined to pay it off, and you should write a will concerning what you owe. 

We ask Allah to help and guide us and you. 

And Allah knows best.