Hosea 11:1 is not a prophecy. It is a history that God called Israel His son out of Egypt.
A prophecy gets fulfilled by the predicted events taking place. How do you fulfill a historical event? Historical events are fulfilled by being repeated.
So Jesus fulfills the historical event of the Exodus by Himself, God's only begotten son, also being called out of Egypt when He was a child.
Matthew also records:
Matthew 2:20 Arise, take to thee the little child and its mother, and go into the land of Israel: for they who sought the life of the little child are dead.
Though Matthew doesn't tell us, the language is an obvious historical repetition, thus fulfillment of:
Exodus 4:19 And Jehovah said to Moses in Midian, Go, return to Egypt; for all the men are dead who sought thy life.
Someone earlier brought up:
Matt 2:17 Then was fulfilled that which was spoken through Jeremias the prophet, saying,
18 A voice has been heard in Rama, weeping, and great lamentation: Rachel weeping for her children, and would not be comforted, because they are not.
Like Hos 11:1, Jer 31:15 is not a prophecy. It is a history, worded in such a way that it would be repeated at Jesus birth by Herod's order to kill the children around Bethlehem.
When the New Testament quotes an OT prophecy as being fulfilled, it needs to be fulfilled in context. When an OT history is fulfilled, it is repeated in a different way such that the words of the OT history apply to what happened in the NT.
I'm just trying to understand what two other stories would be. Joseph gets his family out of Israel and down to Egypt to save their lives. That happens with Jacob's son Joseph and Joseph ("Mary's "husband"). However those are simply parallel stories (vs. prophecies or historical events)? @John Martin
The historical event of Joseph, son of Jacob, going down to Egypt, and thereby saving his family is a historical event, and not a prophecy.
Could you say that Joseph, husband of Mary, fulfilled this when he fled to Egypt to save his family? Maybe.
I think, in order to fulfill a past historical event, as used by Matthew and Jesus, there needs to be a word in the Bible that fits both events, like Hosea 11:1. Maybe there is for this story. The stories of the 2 Josephs do parallel eachother, so I think at least you could say that Joseph, son of Jacob, was a type of Joseph, husband of Mary.
You asked for 2 other OT stories fulfilled in the NT:
1. Baby Moses'
Baby Moses' life was preserved by Miriam when she put him in the ark, watched what would happen, and advised Pharoah's daughter to hire Moses' own mother to nurse him. In this passage, Miriam is called an almah (Exo 2:8), which means an innocent young woman, and is the same word used in Isa 7:14 for "virgin", and quoted by Matthew 1:23. Almah is a rarely used word, so the Holy Spirit had a specific purpose in using the word almah here.
So, in a sense, baby Moses was brought forth by an almah named Miriam, which is the Hebrew equivalent of the name Mary.
This was fulfilled by baby Jesus being brought forth by an Almah named Mary.
Moses' life is especially relevant to Jesus because God said
Deu 18:18 A prophet will I raise up unto them from among their brethren, like unto thee, and will put my words in his mouth, and he shall speak unto them all that I shall command him.
2. David's being betrayed by a trusted friend
David says in Psalm 41:9
9 Even my dear friend,
whom I trusted, who my bread ate
raised his heel against me.
This is not a prophecy. It is a historical event that happened to David. I understand that it refers to Joab, who, at the end of David's life, joined Adonijah's conspiracy to kill Solomon (1Ki 1:5-12) and make Adonijah king.
Jesus says that Judas fulfilled this verse.
Joh 13:18 "I do not speak concerning all of you. I know whom I have chosen; but that the Scripture may be fulfilled, `He who eats bread with Me has lifted up his heel against Me.