Jesus came for sinners and those rejected by society

Scripture references

Matthew 8:1–13 (ASV)

And when he was come down from the mountain, great multitudes followed him. 2And behold, there came to him a leper and worshipped him, saying, Lord, if thou wilt, thou canst make me clean. 3And he stretched forth his hand, and touched him, saying, I will; be thou made clean. And straightway his leprosy was cleansed. 4And Jesus saith unto him, See thou tell no man; but go, show thyself to the priest, and offer the gift that Moses commanded, for a testimony unto them.

5And when he was entered into Capernaum, there came unto him a centurion, beseeching him, 6and saying, Lord, my servant lieth in the house sick of the palsy, grievously tormente...

Matthew 26:6 (ASV)

6Now when Jesus was in Bethany, in the house of Simon the leper,

Luke 5:30 (ASV)

30And the Pharisees and their scribes murmured against his disciples, saying, Why do ye eat and drink with the publicans and sinners?

Luke 7:34 (ASV)

34The Son of man is come eating and drinking; and ye say, Behold, a gluttonous man, and a winebibber, a friend of publicans and sinners!

Stories

Christian Heroes, Then & Now, Corrie ten Boom by Janet & Geoff Benge
After WWII, members of the National Socialist Bond (NSB)—an anti-Semitic body that helped the Nazis to control parts of Holland during the war—were hated by many; they were rendered homeless and spat upon in public. But Corrie remembered that her father had said, on the night he was arrested (because of some of these very people), that he would open his house to anyone in need. So she allowed these outcasts to live in her father's home.
Dr. Baedeker by Robert Sloan Latimer
Mathilda von Wrede, who clearly had God’s heart, was able to translate the warmth of Dr. Baedeker’s Gospel sermon into Finnish. Previously a university professor had given a sterile translation. While the prisoners were unaffected by the professor's words, they were moved to tears when they heard Baedeker address them as “beloved friends.”
Fresh Wind Fresh Fire by Jim Cymbala
David, a homeless man for six years walked up to Jim Cymbala after a church service. Contrary to Jim’s expectation, he wasn't seeking for money; he wanted Jesus in his life. David was led to Christ, rehabilitated, and had his life completely transformed. He got married, became a father and most importantly, a witness for Christ Jesus.
Living on the Devil's Doorstep by Floyd McClung, Jr.
God specifically revealed the details of a prostitute to His servants during a prayer session. After praying for her over a period, she came to the knowledge of Christ surrendering her life to Him.