In that little box at the side of my blog that pops up random limericks from the OEDILF, I just got a limerick for the word "deadlihood". As it's not a word I've ever heard I did a Onelook search to see how many dictionaries it's in. Not many is the answer. Still the OEDILF does aim to include all words, however obscure they may be.
What intrigued me was the meaning. Deadlihood is the state of being dead. (At least according to the obsolete MW definition.) So why isn't livelihood the state of being alive?

(Just being a touch facetious, I know there is no reason why livelihood has to be the opposite of deadlihood. It just damned well ought to be.)

two things:
1) deadlihood = deadlihead
2) deadlihood is not only obs., but rare; i.e., the the OED only has one citation for it
3) there is another sense for livlihood = livliness = livlihead (see 1))

oops, that was three(3) things. I lied.

An obsolete meaning of livelihood is "the quality or state of being lively," according to M-W Online, and an obsolete meaning of lively is "living." The OED Online says that the suffix -hood was originally a distinct word but that it was used so often in combination with other words that it survived only as a suffix. In its own words:

• -hood, suffix
  [ME. -hod (-hode):{em}OE. -hád = OS. -hêd, OHG. -heit.]
  
  Orig. a distinct n., meaning ‘person, personality, sex, condition, quality, rank’ (see HAD n.), which being freely combined with nouns, as in OE. cild-hád child-condition, mæ{asg}{edh}-hád virgin state, pápan hád papal dignity, ceased at length to be used as a separate word, and survived as a mere suffix, and is thus noteworthy as a late example of the process by which suffixes arose. The ME. form was regularly -hôd with open ô, as still in Chaucer; but in the 15th c. it had become close ō (riming in Bokenham's Seyntys with gōd ‘good’), and this duly gave mod.Eng. hood. A parallel suffix, from same root and in same sense, is -HEAD, ME. -hed, -hede, Sc. -heid.
  A considerable number of derivatives in -hood go back to OE. -hád, e.g. bishophood, childhood, priesthood; many are of later origin, either with -hood substituted for the cognate -hede, -head, e.g. falsehood, lustihood, or as analogical formations, in some of which -hood has displaced earlier suffixes. Being a living suffix, -hood can be affixed at will to almost any word denoting a person or concrete thing, and to many adjectives, to express condition or state, so that the number of these derivatives is indefinite. Nonce-formations are numerous:
  
  1599 NASHE Lenten Stuffe 46 Their heauenly hoods in theyr synode thus decreede.
  a1639 W. WHATELY Prototypes I. iv. (1640) 45 It is not man-hood, it is dog-hood, or I may terme it beare-hood.
  1662 SPARROW tr. Behme's Rem. Wks., Apol. conc. Perf. 117 Man in his self-hood and I-hood.
  1876 W. BATHGATE Deep Things of God ii. 19 Acquainted with the great reality of their Soulhood.
  1883 Daily News 3 Oct. 2/2 Believing in the white Aylesburys..as the final expression of duckhood.

Nice to see you again, tsuwm.

Interestingly, there is a livelihead in the OED, too.

quote:

So why isn't livelihood the state of being alive?

Well, this definition from the OED is close: "The course of a person's life, lifetime; kind or manner of life; conduct."