Does a Monster have to survive an attack to yield Tokyo?
When a monster is eliminated while inside Tokyo, they do not yield. Look at the exact phrasing:


  If you are eliminated by an attack on Tokyo, the Monster who attacked
  you automatically takes control of Tokyo.


The rules say "takes control of", not "is yielded," so no yielding happens and the extra damage from Burrowing doesn't occur. Thematically, this makes sense: the monster is dead, and its ability to burrow doesn't help. You aren't yielding to the attacking monster; you're yielding to the sweet embrace of death. (Death takes one damage.)