Will the debtor be regarded as no longer liable if the government or bank waive his debt?

Firstly: 

The Muslim should not be careless about the matter of debt, and he should
not take on any debt except in the case of need. If he does take on a debt,
then when he is able to pay off his debt, he should do so, without any
further delay. If he is not able to pay it off, then he should leave
instructions to his heirs or ask the creditor to let him off. 

Muslim narrated in his Saheeh (1885) from Abu Qataadah (may Allah be
pleased with him) from the Messenger of Allah (blessings and peace of Allah
be upon him) that he stood up before them and said to them: “Jihad for the
sake of Allah and belief in Allah are the best of deeds.” A man stood up and
said: O Messenger of Allah, do you think that if I am killed for the sake of
Allah, my sins will be expiated? The Messenger of Allah (blessings and peace
of Allah be upon him) said: “Yes, if you are killed for the sake of Allah
and you are patient and seek reward, facing (the enemy) and not turning
away.” Then the Messenger of Allah (blessings and peace of Allah be upon
him) said: “What did you say? He said: Do you think that if I am killed for
the sake of Allah, my sins will be expiated? The Messenger of Allah
(blessings and peace of Allah be upon him) said: “Yes, if you are killed for
the sake of Allah and you are patient and seek reward, facing (the enemy)
and not turning away, except debt, for Jibreel (peace be upon him) told me
that.” 

Ibn al-Jawzi (may Allah have mercy on him) said: 

This hadith contains a warning about debt, because the rights of other
people are a serious matter that prevents one from entering Paradise until
they are fulfilled. At the beginning of Islam, the Prophet (blessings and
peace of Allah be upon him) would refuse to offer the funeral prayer for one
who had died in debt. All of that serves as a warning concerning the rights
of other people, so how about if one wrongs them?… 

It is preferable to avoid debt, because in most cases debts are only taken
on for the sake of luxuries.

End quote from Kashf al-Mushkil min Hadeeth as-Saheehayn (2/150) 

Secondly: 

If a person takes on a debt for a good reason, and he intends to pay it
off: 

If he could afford to pay off his debt, but he died before it was due to be
paid, or he was not able to pay it off, but he left instructions to his
heirs to pay off his debt, then he has done what is required of him. 

If he could not afford to pay off his debt, but he intended to pay it off,
then there is the hope that Allah will pay off his debt for him to his
creditor. 

Ahmad (24455) narrated that ‘Aa’ishah said: The Messenger of Allah
(blessings and peace of Allah be upon him) said: “Whoever among my ummah
takes on a debt then tries hard to pay it off, but dies without having done
so, I am his wali (i.e., I am responsible for his debt).”

Classed as saheeh by al-Albaani in Saheeh at-Targheeb (1800). 

Al-Bukhaari (2387) narrated from Abu Hurayrah (may Allah be pleased with
him)  that the Prophet (blessings and peace of Allah be upon him) said:
“Whoever takes people’s wealth, intending to pay it back, Allah will pay it
back on his behalf. Whoever takes people’s wealth, intending to consume it
(and not pay it back), Allah will destroy him.” 

At-Tabaraani narrated in al-Mu‘jam al-Kabeer (1049) that Maymoonah
said: I heard the Prophet (blessings and peace of Allah be upon him) say:
“Whoever takes on a debt, intending to pay it off, Allah will pay it off on
his behalf on the Day of Resurrection.”

Classed as saheeh by al-Albaani in Saheeh al-Jaami‘ (5986). 

“Allah will pay it off on his behalf” means: He will help him to pay it off
in this world or He will compensate his creditor in the Hereafter so he will
be pleased. End quote.

Mirqaat al-Mafaateeh (5/1957)

At-Tirmidhi (1078) narrated that Abu Hurayrah said: The Messenger of Allah
(blessings and peace of Allah be upon him) said: “The believer’s soul is
detained by his debt until it is paid off on his behalf.”

Classed as saheeh by al-Albaani in Saheeh at-Tirmidhi. 

Ash-Shawkaani (may Allah have mercy on him) said: 

This indicates that it is encouraged for heirs to pay off the debts of the
deceased, and it informs them that his soul is detained by his debt until it
is paid off on his behalf. This applies specifically to the one who has
wealth with which his debt may be paid. As for the one who has no wealth but
died intending to pay off his debt, there are hadeeth reports which indicate
that Allah, may He be exalted, will pay it off on his behalf.

End quote from Nayl al-Awtaar (4/30) 

For more information, please see the answer to question no.
118124

Thirdly: 

Bankruptcy does not lead to waiving of debt; rather the debt remains due
until the person is able to pay it off, or someone else pays it off on his
behalf, or the creditor lets him off. 

If the government takes your property as collateral for the debt but it is
not enough, so they wrote off your debt, then one of the following two
scenarios must be the case: 

1.
This debt was owed to
a specific person and was waived in accordance with man-made laws upon proof
of bankruptcy; this debt remains in effect and is not waived, even if the
court has written it off.

See the answer to question no. 127591 

2.
The debt is owed to
the bank or the government, then they took your property as collateral but
it was not sufficient to pay of the debt, so they wrote off the remainder,
because you are unable to pay it off. In this case, you do not have to do
anything, because the creditor has written off the remainder of the debt.
But if they wrote it off unwillingly, rather it was done in accordance with
the law of the land, then the debt remains due and must be paid off when you
are able to do it, or you must leave instructions in your will that it be
paid off, unless you are completely unable to pay it off. In that case, if
your inability to pay it off is for a genuine reason then Allah will pay it
off on your behalf, as mentioned above, and you will not have to do
anything.

In fact, being certain that it is written off willingly in such cases is
difficult or impossible, because the debt in this case is not something owed
to a specific person who could give consent or approval willingly; rather it
is owed to an organisation or body, in which case the one in charge does not
think of the matter in such terms. Rather what usually happens in such cases
is that they are handled in accordance with the law that applies to the
lending body. Hence it is not possible for the bank manager or the like to
waive the debt, even if he wants to do so, unless there is a law which
allows that in such cases. 

But if the debt is owed directly to the government or to a body that is
owned by the government, and the debtor dies without having the means to pay
it off, and the government writes off the debt, then it is waived and the
debtor does not incur any sin or shortcoming, because it is his right over
the government that it should help him in this situation: it should pay off
the debt owed by one who is in difficulty from the public wealth, so how
about if the debt is owed directly to it? 

Al-Bukhaari (8/150) and Muslim (1619) narrated from Abu Hurayrah (may Allah
be pleased with him) that the Prophet (blessings and peace of Allah be upon
him) said: “I am closer to the believers than their own selves. Whoever dies
owing a debt, I will repay it, and whoever leaves behind wealth, it is for
his heirs.” 

Al-Haafiz Ibn Hajar (may Allah have mercy on him) said: 

Was this something that applied only to him, or is it a duty of those in
authority after him? The more correct view is that it continues to be the
case, but the paying off debts is only to be done from the public wealth
allocated for that purpose.

End quote from Fath al-Baari (12/10). See also: Nayl al-Awtaar
(4/31) 

And Allah knows best.