Bingo! Salvation goes no further than those whose sins have been atoned for, paid in full. Its not the cross PLUS faith that saves. Faith is not an addendum to the cross. As Dr. Greg Bahnsen once said, "If justification is grounded in our faith, then it is grounded in something about us."
The cross made salvation possible for all. Our faith makes it actual for the individual.
1Jn 2:2 He Himself is the
atoning sacrifice for our sins, and not only for ours but also
for the sins of the whole world.
but it is only those that have trusted in the risen Christ that will be justified/saved.
Rom 4:5 However, to the one who
does not work,
but believes in Him who justifies the wicked,
his faith is credited as righteousness.
Joh 1:12 But
to all who did receive Him, to those
who believed in His name
, He gave the right
to become children of God
Our justification is grounded in Christ Jesus but we are justified because we believe.
Rom 5:1 Therefore, since we have been
justified through faith, we have
peace with God through our Lord Jesus Christ,
Rom 5:2 through whom
we have gained access by faith into this grace in which we stand. And we rejoice in the hope of the glory of God.
In the NT we find six aspects of Justification
We are justified
by grace (Tit_3:5-7, Eph 2:8-9) — that means we do not deserve it.
We are justified
by faith (Rom_5:1-2, Gal 2:16) — that means that we have to believe on the Lord Jesus Christ to receive it.
We are justified
by blood (Rom_5:9-10, Rom_3:25) — that refers to the price the Savior paid in order that we might be justified.
We are justified
by power (Rom_4:24-25) — the same power that raised the Lord Jesus from the dead.
We are justified
by God (Gal_3:8-9, Rom 3:30) — He is the One who reckons us righteous.
We are justified
by our works (Jas_2:18, Jas_2:24, Jas 2:26) — not meaning that good works earn justification, but that they are the evidence that we have been justified.