All perfect praise be to Allah, The Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallahu ‘alayhi wa sallam, is His slave and Messenger.
Writing down debts and documenting rights is recommended in Islam, but it is not obligatory according to the preponderant opinion of scholars. The person bears no sin if he chooses not to write down the debts. Abu Bakr ibn Al-‘Arabi wrote, "Muslim scholars in different parts of the Muslim world unanimously agreed that the command pertaining to writing down the debts and bringing witnesses for loans and mortgages as stated in the verse indicates recommendation and not obligation, as it instructs us to do what preserves rights and what is more prudent in terms of serving people's interests in the worldly life and the Hereafter. However, none of that is obligatory." [Ahkaam Al-Quran]
Ibn Jareer At-Tabari and a group of early-day scholars held that it is obligatory to write down the debts based on the verse (which means): {O you who have believed, when you contract a debt for a specified term, write it down.} [Quran 2:282]
The correct view in this regard is the opinion of the majority of the scholars, that it is not obligatory to write down the debts. However, this does not mean neglecting or wasting rights; rather, the debtor must pay back his debts. Allah, The Exalted, says (what means): {...And if one of you entrusts another, then let him who is entrusted discharge his trust (faithfully) and let him fear Allah, his Lord...} [Quran 2:283]
As to delaying the settlement of a debt, scholars held different views regarding it, especially the loans. The Maalikis held that it is permissible and that it is binding if it is specified at the time of the contract (agreement). If it is not specified at the time of conducting the contract, it is determined according to the common practice of the community. This is the view which Shaykhul-Islam Ibn Taymiyyah believed to be the most likely correct, as quoted from him by Al-Buhooti in his book Kash-shaaf Al-Qinaa‘. He wrote, "The Shaykh (Ibn Taymiyyah) chose the view that it is valid to delay repayment of the debt and that the payment becomes binding when the agreed-upon time comes whether the debt is in the form of a loan or otherwise, such as the price of a purchased commodity, compensation for damages, or the like, given the general indication of the hadeeth that reads, 'Muslims are bound by their terms and conditions.'" [Kashshaaf Al-Qinaa‘]
If the two parties did not agree on delaying the payment in the contract, the creditor has the right to claim his right whenever he wishes, and the debtor has to fulfill that right if he is solvent (able to repay the debt). If he is insolvent, the creditor is enjoined to give him respite until he becomes solvent.
Allah knows best.