ANSWER: In the kind of family inheritance case you are describing, if the man dies, his biological son produced from his previous marriage would have the right to the greatest share of his father's possessions. Based on the Bible His surviving widow, with whom he had no children, would have to be supported by HER male blood relatives on their property. Note that this principle is likely different from modern laws governing estates in many places around the globe. For example, most U.S. states have laws that grant a surviving widow the right to claim a certain percentage (e.g. one third or one half) of her dead husband's estate regardless of what any written will might specify (a husband cannot disinherit a wife in a will).
There are several examples of family inheritance principles in the Bible. One such interesting principle is that daughters would have a right to their father's possession if there were no sons to carry on the father's name. When the five daughters of Zelophehad asserted that they had a right to a share in their father's future possessions (in this case, land in Canaan) even when he had no sons, Jehovah agreed with them.
|7. It is right what the daughters of Zelophehad speak. You shall surely give them a possession of an inheritance among their father's brothers . . . 8. And you shall speak to the children of Israel, saying, 'When a man dies and has no son, then you shall cause his inheritance to pass to his daughter.' (Numbers 27:7 - 8, HBFV)|
Another Biblical law states that a polygamous man may not prioritize the children of his preferred wife over that of his less preferred or loved wife. He must give a double portion of his possessions to his firstborn son regardless of which of his wives is his mother.
15. If a man has two wives, one beloved and another hated, and they have borne him sons, both the beloved and the hated; and if the firstborn son was of her that was hated, 16. Then it shall be in the day when he makes his sons to inherit what he has, he may not grant firstborn status to the son of the beloved in preference to the son of the hated one - for he is truly the firstborn. 17. But he shall acknowledge the son of the hated as the firstborn by giving him a double portion of all that he has. For he is the beginning of his strength, and the right of the firstborn is his (Deuteronomy 21:15 - 17).
Another interesting example involves Naomi, the mother-in-law of Ruth. Naomi received the land of her husband when he, and both their sons, had died. The problem was that when she wanted to sell the land she could not sell it to just anyone. She had to sell it to a family member who also had to marry Ruth (i.e., the widow of one of Naomi's sons) and to have children by her in her dead husband's name. A close relative turned down his right to buy Naomi's land because he would endanger his own inheritance. As a result, a more distant relative, Boaz, bought that land and willingly acquired Ruth as his wife in the process (See Ruth 4:3 - 11).
Undergirding these principles was the Jubilee land system (Leviticus 25:8 - 10). Every fifty years the land reverted to the original possessors, all the slaves held because they could not pay their debts were freed, and all debts were cancelled. This system prevented the very old, depressing problem of a small elite group of people ending up possessing most of the land in a primarily agricultural economy, such as occurred in the ancient Roman Republic.
Based on the Bible, family inheritance is based on the blood relationship and lineage of the man. In the example you give, the man's physical descendants would inherit what he owned, the priority being given to sons (if any) then to daughters only if no sons exist. The widow would need to be supported by HER physical brothers (or other male blood relatives related to her father) if she never had any children with her deceased husband.