Episode thirteen: Objects In Space

The episode is centered around River as a bounty hunter sneaks aboard Serenity to try and capture her.

As River wanders about the ship occasionally peeking in on everyone, a bounty hunter named Early sneaks about the ship and quickly disables the entire crew and with the exception of Kaylee locks them into their crew quaters.

He then takes Simon for a hostage walkabout as he searches for River. That's when an erie noise booms around the ship with Rivers voice. She boasts about having left her body and become one with the ship and, as he's unable to find her, Early starts to believe it.

In the end, it turns out River got onto Earlys ship but when he realises this Mal has gotten free and takes him out. Thus the last moment of the Firefly series was marked by this bounty hunter floating through space.