Latin is a language
As dead as dead could be.
First it killed the Romans
And now it's killing me.

Quoted from http://www.nzine.co.nz/features/studying_classics.html?Rcat=Culture&Tcat=Education

She was engrossed in her book, but happened to see,
That the man beside her,
as bold as could be,
Grabbed a cookie or two from the bag between,
Which she tried to ignore, to avoid a scene.

Quoted from http://www.bible.org/illus.asp?topic_id=843

Can anyone analyze the structure such as "as dead as (dead) could be" & " as bold as (bold) could be"?

Thank you very much for your help.
(Is it possible to say "I'm tired as tired can be"? and the same for the others)
Pieanne(Is it possible to say "I'm tired as tired can be"? and the same for the others)

I think I usually understand such phrases as implying that there are degrees of tired-ness, boldness, etc., yes-even dead-ness, so that when one adds 'as could be', it means 'to the extreme of ---' or 'to the utmost degree of---'.
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I'll take a crack at it.

Latin is as dead [a language] as dead could be.
This one is easier: as dead as could be is a comparative clause modifying the adjective, dead (the first one). The second dead is a personified quality derived from the adjective and acting as subject of the comparative clause.

The man beside her [is] as bold[ly] [a man] as [bold/man] could be, grabbed a cookie.
This case seems to have several interpretations. To me the most obvious is that the clause as bold[ly] as [bold] could be is a sentence adverbial telling us how the man grabbed the cookies; the embedded comparative clause as [bold]could be modifies the adverb bold[ly], and within it bold is personified as above.

Alternatively, the comparative clause as [bold] could be modifies the preceding adjective bold (as with dead above); OR, the comparative clause as [man] could be performs the same function, with the same ramifications.

Now, I think I had better go and lie down. I am as tired as tired can be.
 pieanne's reply was promoted to an answer.
I think it's possible to say "I'm (as) tired as (tired) can be."
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 davkett's reply was promoted to an answer.
Mister Micawber with the same ramifications.

I like the idea that two interpretations, two different analyses, have the same ramifications.