Most likely that would mean that other members of the household will sooner or later accept Jesus as the Savior, presumably by the influence of their family member and her / his missionary work for them.
On the contrary another point of view could be strengthened by much later appeal of St. Seraphim of Sarov "to again the spirit of peace and therefore, thousands around you will be saved".
It seems more reasonable that individual decision to accept Christ shall be needed in order to obtain salvation. Exceptions may be limited to:
- Baptized infants and baptized children of a household, who could die too early to become able to affirm the decision regarding faith
- Persons with certain disabilities
- It cannot be excluded that our merciful God would restore to salvation, some people, who did not accept the Good News, however, the prayers of family and friends may add for the benefit of those souls.
But overall, in my humble opinion, in order to be saved by Jesus Christ, it is much better to accept an offered salvation from Jesus Christ.