What is the "last" data that get's backed up, when running pg_dump on a live server?
It's the data at the start of the command for an entire database. According to the manpage:


  It makes consistent backups even if the database is being used
  concurrently. pg_dump does not block other users accessing the
  database (readers or writers).


and in SQL Dump:


  Dumps created by pg_dump are internally consistent, meaning, the dump
  represents a snapshot of the database at the time pg_dump began
  running


Dumping in parallel (--jobs) may be problematic with changing data, but only when targeting less recent versions:


  For a consistent backup, the database server needs to support
  synchronized snapshots, a feature that was introduced in PostgreSQL
  9.2


I don't think the output format makes any difference in the rescue operation. Note that for a parallel dump, directory is the only possible format.