The affix kan comes in the sense of 'who must take that' after the word aṃśa 'a share' being in the Accusative -2nd case in construction.,
The word अंश is used in the accusative in the aphorism, showing that the construction must be accusative. The word हारिन् nom. हारी is formed by adding णिनि to the root हृ, the force of the affix being that of \must, or necessity\. See 3.3.170. The word हारिन् will govern accusative and not genitive 2.3.70.
Thus अंश हारी = अंशकः 'an heir', i. e. who is entitled to take a share at partition i.e. a दायादः । अंशकः पुत्रः ॥,