Nibor here. I like the Spartan aspect of screenplays and scripts. They do not tell you everything. You have to imagine it all except for the most bare-bones details. For those of you who prefer more conventional prose, the story is repeated below in that style.
SPOILER ALERT: 'Serenity' Spoiler. Do Not Read if you have not seen the movie.
This takes place after the big fight with Reavers and before the Funeral.
Usual caveats. Done in tribute to the cast and crew and Joss, who gave us some real shiny characters and situations.

INT. HAVEN MED LABS. DAY ZOE walks to the doors. Doors open.

Revealed: JAYNE, gun in hand, stands over WASH in coffin.

JAYNE looks at ZOE. JAYNE looks back at WASH.

ZOE Jayne, what are you doing here?

JAYNE (clears throat)
I ain't got words like Sheppard. Kaylee and Moonbrain gets things said prettier.
Wash got us out of plenty of bad stick. I'm glad we had him... with us.
Won't be easy without him...
(ZOE shifts weight)
for any of us.

ZOE So, why the gun?

JAYNE Some places I been, Fighters get buried with... stuff, I seen swords and (hefting gun)
other things. It's a sign of respect. Just... It's a sign of respect.

JAYNE puts gun alongside WASH. Heads out.

ZOE grips JAYNE'S shoulder.

ZOE He would have appreciated it.
Well, actually, he would have made some... dumb ass stupid joke about it.
I appreciate it, Jayne.
When the time comes, if I have anything to do with seeing to it...
would you want that?

JAYNE (Thinks hard)
Yea... Vera... I'd like her with me... and my Bowie knife. And, I got some vids

ZOE There's only so much room...

JAYNE I guess. Vera, mostly.

ZOE Done.

JAYNE What about you, Zoe?

ZOE If you have any say in it... just bring me back here and set me with Wash.
That's all I want. Deal?

JAYNE Sure... Deal.

JAYNE leaves. ZOE goes to Coffin. Takes WASH'S hand.

Door shuts.

Fade out.

Original 12/02/10 Firefly Fan Fiction - Jayne's Gift.

On the planet Haven Zoe had to see him, one last time.

When the Med room doors slid open, she startled to see Jayne standing over the molecular-cremation chamber that held her late husband, Wash. Jayne had a gun in his hand.

Jayne seemed a bit surprised when he heard the door, but then he saw Zoe and became - unusual for him - relaxed, returning his gaze to the blond-haired pilot lying inside the box.

'Jayne' said Zoe. 'What are you doing here?' It was neither a threat, nor accusation. She was simply confused. She wasn't sure. The emotions of so many years of happiness and dangers shared with her wonderfully annoying, loving man brought to such a terrible end by a Reaver's harpoon still roiled inside her. Her calm was surprising, if thin.

Jayne muttered 'I ain't got words like Sheppard. Kaylee and Moonbrain gets things said prettier. Wash got us out of plenty of bad stick. I'm glad we had him... with us. Won't be easy without him...'

Zoe shifted her weight a bit.

'...for any of us.'

Zoe calmly spoke, 'So, why the gun?'

'Some places I been, Fighters get buried with... stuff, I seen swords and (hefting the gun) other things. It's a sign of respect. Just... it's a sign of respect.'

Laying the gun alongside of Wash, Jayne seemed to not know which way to turn, then went to go out of the room passing Zoe in the doorway. Zoe stopped him with a hand on his shoulder. The grip was strong.

Zoe spoke softly. 'He would have appreciated it, Jayne. Well, actually, he would have made some... dumb-ass stupid joke about it... I appreciate it Jayne. When the time comes, if I have anything to do with it... would you want that?'

Jayne looked at her... his mouth a bit dry. 'Yea... Vera... I'd like her with me... and my Bowie knife. And, I got some vids...'

Zoe interrupted. 'There's only so much room...'

'I guess. Vera, mostly.'

'Done.'

'What about you, Zoe?'

'If you have any say in it, Jayne,... just bring me back here and set me with Wash. Deal?'

'Sure... Deal.'

Jayne broke their gaze and left Zoe alone in the room with her dead husband. Zoe walked slowly over to the coffin, took Wash's hand in hers and held it.

The Med Room door slid shut.

End of Scene.