Can even the worst sinner be saved?
One of the greatest things about Scripture is that it is so honest about who is saved and who can be saved.
The apostle Paul, who wrote 13 of our New Testament books, used his own life to say, "Because of me being saved, you know that God means to be patient with the chief of sinners, because I am the chief of sinners."
He pointed to the fact that he persecuted the church. He threw Christians into jail. He breathed out murders and threatenings, and then he said specifically in 1 Timothy, "God showed patience to me in order that those who were to come to faith might take heart that God will show patience with them."
So my answer is, Yes! Absolutely yes! The most vile, corrupt, consistent sinner can find at the cross of Jesus Christ a sacrifice sufficient to cover all their sins and a righteousness sufficient to replace all their unrighteousness. This is so that when they come to God, they come not in their own righteousness but in the righteousness of Christ; and they come not with their own sins, but with those sins having been forgiven by Jesus Christ.
The worst of sinners can be saved by the all-sufficiency of Christ.