Just as there are causes by virtue of which two persons can inherit from each other, there are also impediments that could hinder inheritance between them. Those impediments might be summed up as follows:
First impediment: Difference in religion
If the deceased follows a religion and the heir follows another religion, the difference in religion between two persons impedes them from inheriting from each other. Such difference in religion takes several forms including:
The deceased is a Muslim and the heir is a disbeliever, say a Jew, a Christian or belonging to any religion of disbelief. In this case, the disbeliever does not inherit from his Muslim relative. There is no difference of opinion over this fact among scholars in general, due to the following Hadeeth (narration): "No Muslim inherits from a disbeliever and no disbeliever inherits from a Muslim." [Al-Bukhari]
The deceased is a disbeliever and the heir is a Muslim. In this case, the Muslim should not inherit (from the property of) his disbelieving relative, according to the opinion of the majority of scholars, who base their opinion on the previous Hadeeth.
The deceased is a disbeliever, belonging to a particular religion, and the heir is also a disbeliever, but belonging to another religion. In this case, they should not inherit from each other, due to the Hadeeth: "No people belonging to two different religions should inherit from each other." [Abu Daawood and At-Tirmithi]
There are, indeed, juristic differences as to the classification of religion. According to some scholars, disbelief as a whole is regarded as one religion; and according to others, there are three religions (apart from Islam): Judaism is a religion, Christianity is a religion and all other religions are regarded as one religion.
Second impediment: Killing
Killing is to commit an act that terminates the life of another person. It means that the murderer never inherits from the murdered person. If a son kills his father, he will not be entitled to inherit his property.
It is well known that killing is of different kinds: for instance, the murder with no just cause, the intentional killing, semi-intentional killing, killing by mistake; and killing with just cause (like killing in implementation of legal retribution). However, scholars agree on the fact that murder is among the impediments of inheritance, due to the Hadeeth: "The killer has nothing to inherit, and if he (the deceased) has no heir, his heir should be the closest relative to him. The killer inherits nothing." [Abu Daawood]
However, there is a difference of opinion among the scholars of Fiqh (Islamic jurisprudence) as to whether or not some forms of killing could impede the killer from inheriting.
Third impediment: Slavery
It is the state of being a slave to another. The slave never inherits the property of the free man, since the slave does not possess property.