Salvation is a personal matter. Each person is to repent and be baptised (Acts 2:38), and we are told to “work out your own salvation with fear and trembling” (Philippians 2:12). Also, judgement will be on an individual basis:
“As I live, says the Lord, every knee shall bow to me, and every tongue shall confess to God.”
So then each of us will give an account of himself to God. (Romans 14:11-12)
So it is not possible to be saved by simply living with a believer.
However, a believer can have considerable influence on other members of a household. For example, Peter wrote to believing women:
Likewise, wives, be subject to your own husbands, so that even if some do not obey the word, they may be won without a word by the conduct of their wives, when they see your respectful and pure conduct. (1 Peter 3:1-2)
A similar idea is found in Paul’s letter to the church in Corinth:
For the unbelieving husband is made holy because of his wife, and the unbelieving wife is made holy because of her husband. Otherwise your children would be unclean, but as it is, they are holy. (1 Corinthians 7:14)
Being “made holy” is not the same thing as being saved, but this passage does show that unbelievers who live in the same household as believers are treated differently by God compared to other unbelievers.