There are two situations where I've used this.
1. Migrations. We have some fairly large databases and the plan was to keep the old system online for as long as possible. So.... we did a full backup while everyone was online and, about an hour before the migration time slot was to begin, we took DIF backups. At the appointed time, we took the Tail Log backups which prevents anyone from using the database and captures all of the latest data in the log file. Then we did our restores. Saved a huge amount of time doing the backups and saved us from having to do "online merges" of data, which are always a pain.
2. The MDF failed but the log file is still viable. It's standard operating procedure that if a database MDF/NDF file goes corruption, you should do a Tail Log backup to capture as much data as possible and take the ailing database into a restoring mode so no one can use it until you've done a proper restore.