Judges 4:21 describes the death of Sisera:
On the other hand, this is Judges 5:26-27:
So there's a tension between the verse where he's asleep, and the verse where he "sank" and "fell". However, this doesn't appear to be a real problem, because these words are part of a song being sung by Deborah and Barak. There's no obvious reason to think such a song would be particularly accurate.
On the other hand, the quoted song is very long. It might seem reasonable that, since the Bible so extensively quotes this song, it therefore endorses the contents of the song as accurate. It might also seem that the Holy Spirit is speaking through the singers.
Perhaps a better solution is that talk of "falling" is simply a metaphor for death.