Say someone becomes niftar and owes a petty sum (under 100 currency units) is his next-of-kin chayav to pay his debts under halachah?
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These things can get complicated, but generally speaking the children are obligated to pay off the father's debts from either land or chattel IF the father left them an inheritance of at least that size. If the father did not leave any inheritance, the children are not obligated to pay anything. (Shulchan Arukh CM 107:1)
If the debt is from a loan which was made orally and without documentation (milveh 'al peh), the children are only obligated if it can be ascertained with certainty that the father never paid. (ibid 108:1)