All perfect praise be to Allah the Lord of the Worlds. May Allah`s peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
When someone dies, the first thing to do is to pay the expenses of the funeral from his/her estate and if a relative volunteered to pay for that, then he may do so. After that his/her debts are paid off, be they owed to Allah, such as expiations, Zakah and the like or to individuals, public entities or institutions. This is because the Prophet (PBUH) said, "The soul of the deceased believer remains pending on account of the debt till it (the debt) is repaid."{Related by Tirmithi}.
According to scholars of Hadith, "The soul of the deceased believer remains pending on account of the debt" means that his soul is suspended by the debt he owed. Al-Iraqi said, it is suspended in the sense that it is awaiting whether its debt will be settled or not."{Qoot al-moghtathi ala Jami`e Attirmithi, 1/326}.
Water bills for which the deceased is liable are part of the debt that must be paid off and this matter shouldn`t be taken lightly under the pretext that people are partners in water, or any other excuse.
However, if the deceased had no estate and his/her heirs or some of them wanted to pay off the debt from their own wealth as a donation, then this is recommended to clear him/her from liability. Nonetheless, settling that debt isn`t an obligation upon them. The evidence on this is that Salama b. al-Akwa' said: While we were sitting with the Prophet a bier was brought along and the Prophet was asked to pray over it. He asked whether the dead man owed anything and when he was told that he did not he prayed over it. Another bier was brought along later, and when he asked whether the dead man owed anything and was told that he did, he asked whether he had left anything. On being told that he had left three dinars he prayed over the bier. A third was brought along later, and when he asked whether the dead man owed anything and was told that he owed three dinars, he asked whether he had left anything. On being told that he had not, he ordered them to pray over their friend; but when Abu Qatada said, “Pray over him, Messenger of God, and I shall be responsible for his debt,” he prayed over him. {Related by Bukhari}.
In conclusion, debts of the deceased must be paid from his/her estate if there is any. If not, and his/her heirs or some of them volunteered to pay them off in the form of a donation to clear him/her from liability before Almighty Allah, then they will be rewarded for that. Moreover, this is considered a good deed gifted to the deceased particularly if the latter is a parent; in which case settling his/her debt is an act of dutifulness to him/her after their passing away. And Allah the Almighty knows best.
