The fuel pressure regulator does what it's name implies - it regulates fuel pressure. The fuel pump puts out a constant amount of fuel at a constant pressure, even though the engine will need varying amounts of fuel depending on operating conditions. The fuel pressure regulator keeps too much guel from getting to the engine when it is not needed.
When the engine it turned off, it should maintain fuel pressure without bleeding down. On a cold start, it would supply full pressure to enable a start.