If he dies and does not leave behind anyone but a brother or sister through his mother
Question

                If 1/6th property of kalala is given to either of his/her ikyafi brother or sister then what happens to the remaining property of the kalala ?.
Praise be to Allah.
      Kalaalah refers to a person who dies and has no father or 
      son. If he has a brother or a sister through his mother, each of them gets 
      one-sixth (of the estate), and if they are more than that then they share 
      one third, because Allah, may He be exalted, says (interpretation of the 
      meaning):

    “If the man or woman whose 
    inheritance is in question has left neither ascendants nor descendants, but 
    has left a brother or a sister, each one of the two gets a sixth; but if 
    more than two, they share in a third”

    [al-Nisa’ 4:12]. 

    If he had a wife, she gets one half. 

    If he had a full brother, then he gets the entire estate or 
    what is left, by virtue of being a male relative on the father’s side 
    (ta‘seeb), after those who are entitled to allotted shares have received 
    them, if there are any such heirs. 

    If he has a full sister, then she gets half, and if there are 
    two sisters then they get two thirds, because Allah, may He be exalted, says 
    (interpretation of the meaning):

    “They ask you for a legal 
    verdict. Say: "Allâh directs (thus) about Al-Kalâlah (those who leave 
    neither descendants nor ascendants as heirs). If it is a man that dies, 
    leaving a sister, but no child, she shall have half the inheritance. If 
    (such a deceased was) a woman, who left no child, her brother takes her 
    inheritance. If there are two sisters, they shall have two-thirds of the 
    inheritance; if there are brothers and sisters, the male will have twice the 
    share of the female.”

    [al-Nisa’ 4:176]. 

    If he only has a brother or a sister through the mother, then 
    he or she takes one-sixth as an allotted share and the rest of the estate 
    comes to him (or her) according to the Hanafis and Hanbalis. Thus he (or 
    she) takes the entire estate.  

    Maalik and al-Shaafa‘i were of the view that the remainder of 
    the estate should go to the bayt al-maal if there are no male relatives on 
    the father’s side (‘asbah). 

    Ibn Qudaamah (may Allah have mercy on him) said in 
    al-Mughni (6/186): To sum up, if the deceased did not leave behind any 
    heir except those who are entitled to an allotted share, such as daughters 
    or sisters or grandmothers, and there is some wealth left over, then what is 
    left over from the allotted shares should be given to them on the same basis 
    as the allotted shares, except in the case of a husband or wife. This was 
    narrated from ‘Umar, ‘Ali, Ibn Mas‘ood and Ibn ‘Abbaas (may Allah be pleased 
    with him). It was also narrated from al-Hasan, Ibn Sireen, Shurayh, ‘Ata’, 
    Mujaahid, al-Thawri, and Abu Haneefah and his companions. Ibn Suraaqah said: 
    Things are done on this basis now in the regions. 

    Zayd ibn Thaabit was of the view that what is left over from 
    the allotted shares should go to the bayt al-maal and no one should be given 
    more than his allotted share. This was also the view of Maalik, al-Awzaa‘i 
    and al-Shaafa‘i (may Allah be pleased with them). End quote. 

    And he said: With regard to the spouses, what is left over 
    (after giving the allotted shares) should not be given to them, according to 
    the consensus of the scholars, but it was narrated from ‘Uthmaan (may Allah 
    be pleased with him) that he did give the left-over wealth to the husband, 
    but perhaps he was a relative on the father’s side (‘asbah) or on the 
    mother’s side (dhu rahm), so he gave that to him or he gave it from the bayt 
    al-maal and not by way of inheritance. End quote. 

    When it comes to matters of inheritance, it is important to 
    ask about every case according to what the deceased has left behind in his 
    estate, lest there be any error in applying the rulings in a given case. 

    And Allah knows best.