At times people can feel so tainted with sin and guilt that they doubt that Jesus can help them. John Piper in Desiring God writes the following…
“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,”
“How true it is, and how I long that everyone should know it, that Christ Jesus came into the world to save sinners—and I was the greatest of them all. But God had mercy on me so that Christ Jesus could use me as an example to show everyone how patient he is with even the worst sinners, so that others will realize that they, too, can have everlasting life. Glory and honour to God forever and ever. He is the King of the ages, the unseen one who never dies; he alone is God, and full of wisdom. Amen.” 1 Timothy 1:15-17, TLB.
“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.” John Piper.
This passage and example from Paul can help us come to know Jesus and it can also help us to never give up on anyone. Be in constant prayer for your salvation and for the salvation of those you are praying for.