The 300 inmates were the firmest (most unbendable) in all of America.

the most incorrigible

I'd say here; "firm" is definitely wrong here, and unbendable seems odd - wills are unbendable, but generally not people

Also possible: ... were the most hardened criminals ...

incorrigible would mean impervious to correction by punishment, which is not necessarily what the German word "unbeugsam" means. "Unbeugsam" usually refers to a strong will, therefore unbendable or firm (marked by firm determination or resolution; not shakable). That could also refer to a strong moral code.
"Incorrigible" would be "unverbesserlich".

rigid

I agree with dude

Here they refer to a "firm prisoner". I can give you a few more examples, can you give me one that says you cannot use it?

a whopping 346 hits for "firm prisoner" doesn't exactly make this a common phrase, especially when quite a few of them turn int "the firm's prisoner." :-)

obdurate

hard-core - common today. Tony Blair - he used it, I mean

unyielding

Oh so now anything that doesn't get "enough" Google-hits is therefore "definitely wrong" even if it appears in legal texts and history books ("These religious prisoners were the firmest and most unbreakable")? Come on, what sort of arguing is that?

whatever; I'm not going to argue with someone who doesn't even seem to have a native tongue. :-)

besides, it's Sunday.

agree 100% with Dude - "firm prisoner" and "firmest prisoners" can't be compared - different contexts

They were 300 of the most unrelenting inmates in the USA.

"firm", "unbending": geht Beides nicht. Wenn es nicht "unverbesserlich" sein soll, bin ich für "hardened".

wie wär's mit:
most rebellious, most insubordinate, most defiant

the prisoners could be firm if they have exercise equipment like dumb bells, etc.