All perfect praise be to Allah the Lord of The Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
Killing someone unintentionally is accidental killing. Allah the Almighty Says {What means}: " Never should a believer kill a believer; but (If it so happens) by mistake, (Compensation is due): If one (so) kills a believer, it is ordained that he should free a believing slave, and pay compensation to the deceased’s family, unless they remit it freely." {An-Nisaa`, 92}. According to scholarly opinion, Diyah (Blood money) and Kafarah (Expiation) are due on the killer in case of accidental killing.
As for the one who kills by accident, there is a difference of scholarly opinion. The majority of the Hanafi, Shafie, and Hanbali scholars stated that the killer doesn`t inherit from the killed.
Al-Sarkhasi stated: "The one who kills unjustly doesn`t inherit from the killed, whether the killing is deliberate or accidental." {Al-Mabsout, vol.47/pp.30}.
Al-Shirbini said: "The killer never inherits the killed. The proof of this is the Hadith narrated by At-Tirmithi (The killer does not inherit). If this killer is allowed to inherit the deceased then people would start killing their relatives to expedite inheriting them. Therefore, it is an act of wisdom to deprive him from the inheritance. This is whether the killing is accidental or intentional." {Moghni al-Mohtaj, vol.4/pp.47}.
"Unjust Killing, be it intentional, accidental, or semi-intentional, deprives the killer from inheriting the deceased." {Khashaf al-Khinaa`, vol.4/pp.492}.
As for the Maliki scholars, they are of the view that the one who kills by accident may inherit from the estate of the killed. Sheik al-Dardeer stated in his book {Al-Shareh al-Kabeer, vol.4/pp.486}: "The one who kills by accident may not inherit from the Diyah (blood money) of the deceased but may inherit from the estate."
The Jordanian Personal Status Law adopted this view where article (281) stated: "The one who kills deliberately may not inherit from the deceased. Thus, the law allows the one who kills by accident to inherit from the killed."
In conclusion, firearms should be handled with utmost care to avoid such unfortunate incidents. And Allah the Almighty Knows Best.