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 is His slave and Messenger.
If a Muslim abandons the prayer because he denies that it is obligatory, according to the scholarly consensus, it is considered an act of Kufr (disbelief) that takes the doer out of the fold of Islam – Allah forbids. The statements of the jurists regarding the one who takes the property of an apostate when he dies apply to him. Al-Mawsoo‘ah Al-Fiqhiyyah reads: “Jurists held three different opinions regarding the wealth of an apostate if he is killed or dies while adhering to apostasy:
1 – All his wealth goes to Bayt-ul-Maal (Muslim public treasury), and this is the view of Imaams Maalik, Ash-Shaafi’i, and Ahmad.
2 – His wealth goes to his Muslim heirs, whether he earned it during his Islam or apostasy, and this is the view of Abu Yoosuf and Muhammad (the two companions of Abu Haneefah).
3 – The wealth he earned as a Muslim goes to his Muslim heirs, and what he earned as an apostate goes to Bayt-ul-Maal, and this is the view of Abu Haneefah.” [End of quote]
However, if he abandons the prayer out of laziness while believing in its obligation, then most of the jurists are of the view that he is a Faasiq (defiantly disobedient) and perpetrator of a major sin, but not a disbeliever who is outside the fold of Islam. Accordingly, if he dies in such a state, the rulings on Faasiq Muslims apply to him; he should be shrouded and the funeral prayer should be performed over him, and he is entitled to inherit and his (Muslim) heirs inherit from him. The ruling in this regard is further confirmed if he performs the prayers occasionally (and does not abandon it altogether).
As for the fact that he left ill-gotten wealth, the jurists held different opinions regarding the heirs who inherit ill-gotten wealth, as to whether or not it is lawful for them. There are two opinions in this regard, and the one adopted here at Islamweb is that it is unlawful for the heirs. Ibn Rushd said in Al-Muqaddimaat Al-Mumahhidaat (2/159): “The act of inheriting does not make ill-gotten wealth lawful for the heirs, and this is the valid opinion that is entailed by deduction. It was narrated on the authority of some early scholars that the act of inheriting makes the ill-gotten wealth lawful for the heirs, but this is not correct.” [End of quote]
An-Nawawi said: “Whoever inherits wealth and does not know how the deceased earned it (i.e. whether its source was lawful or unlawful), and there are no signs indicative of its lawfulness or unlawfulness, then, according to the scholarly consensus of opinion, it is lawful (for the heirs). If the heir knows that the wealth contains an unlawful portion and he doubts the amount of that unlawful portion, he should make an estimate of it to the best of his ability and spend that estimated sum in charity.” [End of quote, from Al-Majmoo‘ (9/428)]
Accordingly, the wealth earned by the deceased through selling alcohol is unlawful for the mentioned heirs. They are only entitled to inherit the amount of his capital with which he traded but not the profits he earned from that trade. We do not believe that they are obliged to sell the inherited house because the unlawfulness is not related to the house itself, and the liability rather falls upon the owner who had obtained the unlawful wealth (i.e., he bears the sin for it).
Allah Knows best.