Very interesting data and question.  Note that English is somewhat similar to German:

(1) 	a. *die a death
 	b. die a miserable death

Note also that along with b., the failure to take a cognate object is a test for 
unaccusativity:

b'. an unaccusative verb may not take a cognate-object (unlike unergative verbs: dream
a dream, laugh a hearty laugh, etc.) (this from a handout by David Pesetsky accompanying
a lecture on unaccusativity by Barbare Partee, 2003 -- I haven't seen it elsewhere)

Any idea why b' is overridden in the case of die-co?

A couple of other comments:

RE d. below, note that in Greek at least, in addition to cognate objects whose sense
is the same as that of the verb, there are others where the sense is merely related.

(2)	a. nike:n nika:n 'to gain a victory'
 	b. maxe:n nika:n 'to win a battle'

Also in connection with d., but a different part of it, note first that some
cognate-object verbs can have two objects (clearly a 'causative' transitive in the
case of (4) and possibly the same in (3)):

(3)	Mele:tos me egrapsato te:n graphe:n taute:n
 	M. me(acc) brought-suit the(acc) suit(acc) this(acc)
 	'Meletus brought this indictment against me'

(4)	o:rko:sav pantas tous stratio:tas tous megistous orkous
 	made-swear-3pl all the soldiers the strongest oaths
 	'they made all the soldiers swear the strongs oaths'
 	(both objects are accusative in case)

Is there a WG analysis of causative verbs?

Again with c-o verbs which are not unaccusative, the cognate accusative
may become a subject, indicating that it is an object and not an
adverbial adjunct:

(5)	a.	ton kindunon kinduneuei 's/he runs the risk'
 		the(acc) risk(acc) risks
 	b.	ho kindunos kinduneuetai 'the risk is encountered'
 		the(nom) risk(nom) is-risked-3sg

Chet

On Mon, 18 Apr 2005, Richard Hudson wrote:

> Dear WG,
> This message has just appeared on the LFG list. It includes a very 
> interesting datum from German, where a verb which is so intransitive that it 
> takes the auxiliary 'be', usually used only with  unaccusatives, nevertheless 
> takes an accusative object. How about this analysis?
> a. a verb has no object.
> b. an unaccusative verb takes 'be' as auxiliary.
> c. 'die' is an unaccusative verb.
> d. a cognate-object verb has an object (whose sense is the same as that of 
> the verb).
> e. 'die-co' is-a 'die' and cognate-object verb.
> Does this work and explain the pattern?
>   Dick
>
> John Peterson wrote:
>
>> Hello!
>> 
>> I'm sending this inquiry on behalf of a friend who is not a member of this
>> list.
>> Is anyone aware of literature in an LFG-format which deals with "cognate
>> objects" or "figura etymologica" with intransitive verbs of the type in
>> the following examples:
>> 
>> Er ist den Heldentod gestorben. (German)
>> He died a heroic death / a hero's death.
>> 
>> (Note: The object need not derive from the same lexical morpheme as the
>> verb, as in the German sterb- 'die' and Tod 'death' as long as the two are
>> semantically very similar to one another.)
>> 
>> At issue here is how to deal with these apparent "objects", since the verb
>> in this case the verb is intransitive. Note that, at least in general, if
>> the "object" is not modified, the construction is not grammatical:
>> 
>> *He died a death. / *Er ist den Tod gestorben.
>> 
>> This makes them look more like adverbs than objects (e.g. "He died
>> heroically") so that they could be considered adjuncts. Any ideas?
>> 
>> All the best,
>> John
>> 
>> 
>> --
>> John Peterson
>> FB 7, Sprachwissenschaft
>> Universität Osnabrück
>> D-49069 Osnabrück
>> Germany
>> Telephone: (+49) (0)541-969 4252
>> Telefax: (+49) (0)541-969 4256
>> Homepage: http://www.SouthAsiaBibliography.de/
>> 
>> 
>> 
>> 
>
> -- 
> Richard Hudson, FBA,
> Emeritus Professor of Linguistics,
> University College London
> www.phon.ucl.ac.uk/home/dick/home.htm
>