What about his Mother? Father? Sister? etc
I can't find any commentary on that verse by Rashi. Hmm
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It is talking about those relatives who would normally inherit his property. Lineage follows the paternal (male) line. Thus, moving up the line of inheritance, if his "brothers" cannot redeem him, the next closest line are the brothers of his father (his uncle) and the uncle's descendants (his cousins).
For example see the halacha of the ancestral portion in pesukim 23-24 which deals with returning the ancestral land to the original owner (and tribe). Also Pasuk 10
Thanks to @DanF for pointing out that that the discussion of Mas'ei 36:4-9 shows that the yovel is connected to the inheritance and follows the shvatim. Similarly a person is considered as part of his shevet and the redemption spoken of traces along back to the closest relative to the person being redeemed within the shevet. Normally, the yovel returns property to its owner or his heirs. If he has no sons (or daughters), then it moves back up the male line. In the normal case all heirs (or yovel return recipients) are male in this way. That is why the uncles and cousins are the ones mentioned as the nearest kinsman in the absence of brothers.
you shall return, each man to his property,_ and you shall return, each man to his family.
Rav Hirsch points out that this means that it must return to the tribe (at the least) and to the appropriate owner of the land (which is the sons, brother, uncles, cousins, etc.).
The Art scroll chumash summarises as
47 - 55 Jews owned by non-Jews. The ultimate degradation is for a Jew to be sold as a slave to a non-Jewish resident of Eretz Yisrael. In that unpleasant case, the Torah places a responsibility upon his knsmen to redeem him, but they must do so without depriving the owner of his legitimate rights.
Since the definition of kinsmen is through the paternal line and it is analogous the the land (as part of the shevet) the Torah here refers to the closest (non-immediate) relatives. That is pasuk 48 had brothers as the most immediate, and then pasuk 49 is the next level away from his father (his father's brother) and his immediate heirs.
@DanielF hinted correctly. The previous verse explicitly says, "One of his brothers". The end of the current verse includes everyone by saying, "Or one of his kin from his family".
Also, see Da'at Zekenim commentary - "uncle" is a metaphor for G-d himself, and "cousin" is a metaphor for the Messianic King.