Psalms of Solomon 9:5
4 We are free to choose and do what we will to do right or wrong in how we live our lives; in your justice you watch mortals closely. 5 Those who do what is right save up life for themselves with the Lord, and those doing what is wrong cause their own lives to be destroyed; for the Lord's righteous judgments come down on man and household. 6 To whom will you be kind, O God, except to those who appeal to the Lord? He will cleanse from sin the person who both confesses and publically acknowledges it. For all of these things we are ashamed, and we are embarrassed.
Acts 16:31
27 When the jailer woke up and saw the doors of the prison standing open, he drew his sword and was about to kill himself because he assumed the prisoners had escaped. 28 But Paul called out loudly, “Do not harm yourself, for we are all here!” 29 Calling for lights, the jailer rushed in and fell down trembling at the feet of Paul and Silas. 30 Then he brought them outside and asked, “Sirs, what must I do to be saved?” 31 They replied, “Believe in the Lord Jesus and you will be saved, you and your household.” 32 Then they spoke the word of the Lord to him, along with all those who were in his house. 33 At that hour of the night he took them and washed their wounds; then he and all his family were baptized right away.
Notes and References
"... That God’s name was invoked over God’s people, city, or house was common Old Testament idiom, contrasting with the Gentiles, who lacked this special designation (Isaiah 63:19); it applies to “Israel’s covenant status” in many early Jewish texts (e.g., Sirach 36:17; 2 Maccabees 8:15; Baruch 2:15; Psalms of Solomon 9) ... Paul and Silas expect that the family will convert with the head of the household, which was usually the case (cf. Acts 10:2), although other members of the household were sometimes converted first (1 Cor 7:12–16; 1 Pet 3:1). The text is hardly an unconditional guarantee for the conversion of family members (cf. Luke 12:51–53; 14:26; 18:29); rather, in context it implies the expectation (again based on the normal cultural pattern) that other members will be saved because they also will believe (Acts 16:31). Thus the missionaries proceed to speak to the members of the household (16:32), who also believe and receive baptism (16:33–34). Respectable patrons of families were to rule their families, and grave embarrassment followed if they failed to do so. The behavior of family members reflected on fathers politically. The paterfamilias in a Roman household had exorbitant legal power, but this was mitigated in practice. Still, people evaluated fathers by their children’s religious decisions ..."
Keener, Craig S. Acts: An Exegetical Commentary, Volume 3 (p. 206, 488) Baker Academic, 2014