Today we fast in commemoration of Nebuchadnezzar’s seige of Jerusalem which resulted in the destruction of the First Bet HaMikdash. The fast day is simply called Asara BaTevet. strange thing about the Tenth of Tevet is that when it falls out on a Friday, we don’t push it off or push it back, We fast on Friday unlike other fasts. And Avudraham suggests that were it to fall out on Shabbat, we would even fast on Shabbat and we only do that when Yom Kippur falls on Shabbat. Why? We commemorate the siege only while on other days we remember the more difficult anniversaries of the breaking of the walls and the destruction itself. What makes the Tenth of Tevet different?  

This fast almost always falls during the week we read Vayechi. Vayechi Yaakov which translates as Jacob lived seems to be more about Jacob dying rather than living.  

The weekly portions always are demarcated; they begin either on a new line, or on the same line as the end of the previous portion but after a space large enough to have nine letters written in it. Vayechi is an exception, in that there is no space at all between the end of last week's parsha, Vayigash, and the beginning of Vayechi - the last word of Vayigash is followed immediately by the first word of Vayechi. 

 Rashi quotes two explanations of this unique phenomenon. 'Why is this parsha 'stumah' [closed, or sealed, i.e., written immediately after the end of the preceding parsha with no space in between]? Because once Jacob died, the eyes and hearts of the Israelites were closed by the oppression of their subjugation, for it was then that they [the Egyptians] began to subjugate them. Another explanation is that Jacob wanted to reveal the “end” to his sons, but it was closed to him.'