One grammatical quirk of the 'rural' dialect in Firefly is restrictive relative clauses "them that" as in:

If that's what you think of this life, then you can't think much of them that choose it, can you? -- Kaylee

Or "them as":

Just get us some passengers. Them as can pay. -- Mal
Small crew, them as feel the need to be free - Mal

To see whether this was something English used to do or something Whedon made up, we can look at the N-Gram viewer:

Them that are, Them as are:

Them that can, Them as can:

So "them that/as verb" appears to be something English used to do a lot more of.

People pretty much don't use that construction now, unless they're mimicing Firefly, so how did we lose it? It looks to me like the main change was using "those" in place of "them":

Them who are, Those who are:

Them who can, Those who can:

Them who do, Those who do:

It appears "those who" has always been much more popular (but "those that" is catching up):