According to rabbinic commentary, the assembly which Moses convenes at the beginning of Parashat Vayakhel took place on 11 Tishri, the day after Yom Kippur.
In a sense there is a second day of Yom Kippur. Not another day of fasting, which would be an unbearable strain for most people, but a second day of self-searching.
In the Book of Jonah, the Yom Kippur afternoon haftarah, the prophet watches the city of Nineveh to see what is going to happen after the drama of his call to repentance.
On 11 Tishri God specially watches the people of Israel to see if the Day of Atonement has done its work and whether they have maintained the serious sense of dedication which marked the fast day.