The prophet Jeremiah, who predicted the Babylonian captivity, associates it with the number seven.
11 'And this whole land shall be a desolation and a horror, and these nations shall serve the king of Babylon seventy years.
12 'Then it will be when seventy years are completed I will punish the king of Babylon and that nation,' declares the LORD, 'for their iniquity, and the land of the Chaldeans; and I will make it an everlasting desolation.
(Jer. 25:11-12 NAS)
The author of Chronicles refers back to the prophet's words, and makes explicit, what is subtle in the original prophecy, the connection with the Shemitah system is made explicit in Chronicles.
17 Therefore He brought up against them the king of the Chaldeans … 20 And those who had escaped from the sword he carried away to Babylon; and they were servants to him and to his sons until the rule of the kingdom of Persia,
21 to fulfill the word of the LORD by the mouth of Jeremiah, until the land had enjoyed its sabbaths. All the days of its desolation it kept sabbath until seventy years were complete. (2 Chr. 36:17-21 NAS)
The prophet Daniel takes that idea and extends it further. He lived in the exile situation which Jeremiah had predicted. God revealed to him that the period of exile would not be just seven, but seventy times seven.
"1 In the first year of Darius the son of Ahasuerus, of Median descent, who was made king over the kingdom of the Chaldeans--
2 in the first year of his reign I, Daniel, observed in the books the number of the years which was revealed as the word of the LORD to Jeremiah the prophet for the completion of the desolations of Jerusalem, namely, seventy years...
24 "Seventy weeks have been decreed for your people and your holy city, to finish the transgression, to make an end of sin, to make atonement for iniquity, to bring in everlasting righteousness, to seal up vision and prophecy, and to anoint the most holy place..."
(Dan. 9:1-24 NAS)
The Hebrew words for seventy weeks are almost exactly the same. In other words, 'weeks' is 'seven'. Literally, this is 'seventy sevens'. This puts Jesus' statement to Peter about forgiving 'seventy times seven' in a new light (or actually in a very old light).
The prophet Isaiah takes this theme -- release of debt captives, a Jubilee theme -- and associates it with the coming Messiah.
NAS Isaiah 61:1 The Spirit of the Lord God is upon me, Because the LORD has anointed me To bring good news to the afflicted; He has sent me to bind up the brokenhearted, To proclaim liberty to captives, And freedom to prisoners;
2 To proclaim the favorable year of the LORD, And the day of vengeance of our God; To comfort all who mourn,
(Isa. 61:1-3 NAS)
Note how the liberty of captives harkens back to Leviticus, thereby aligning debt forgiveness, end of exile and the Messiah:
39 'And if a countryman of yours becomes so poor with regard to you that he sells himself to you, you shall not subject him to a slave's service.
40 'He shall be with you as a hired man, as if he were a sojourner; he shall serve with you until the year of jubilee.
41 'He shall then go out from you, he and his sons with him, and shall go back to his family, that he may return to the property of his forefathers.
(Lev. 25:39-41 NAS)