Scriptures have listed who can perform rites for one who has no son. If there is no son, then the daughter’s son is eligible foremost to perform rituals; if he is not available, the son-in-law can perform the rituals by getting the grass from the daughter of the demised as the daughter is the kartha here.
The grandson can perform the annual ceremony if there is no son in the family; if there is no grandson, then the son-in-law can perform the ceremony by accepting the darbha from the daughter of the deceased. When the son-in-law does so, it becomes his duty to do it every year.
The karmic effects of a grandfather’s sins or virtues do not directly pass on to the next generation; we undergo experiences as per our karmic effects. We also get associated with each other through karma. When a grandfather passes away after committing sins it is not a must that the sons or grandsons acquire his sins. He has to undergo whatever he has done. It is due to the effect of karma that the son or grandson takes birth by being related to him. The effects of karma are real, and one has to undergo the effects as per one’s karma, hence the birth.
Any physical relation is according to one’s karma including husband and wife. Emperuman associates each one as per their karmic bond and it takes effect accordingly.