Although there are no natlangs known to lack the noun-verb distinction, nor do I know of any conlang, it is still a theoretical possibility for a language to lack such a distinction.
One possible method of destroying the distinction would be to create a verb class similar to the present participle that would be able to act as a modifier to another verb, essentially creating a long chain of complicated verbs referencing a noun without said noun actually appearing. The noun would instead be substituted by a verb participle as the patient/actor. One consequence of this would be that the language would also lack adjectives, them having been completely replaced by adverbs.
Some possible examples could be:
- humaningly sitting falls from blocking
- ~~Be.human+ADV to.sit+SUBSTANTIATIVE-MOOD to.fall+PRES from to.block+SUBSTANTIATIVE-MOOD
This, however, only blurs the boundary a little bit.
A few conlangers have attempted to build a language with only one part of speech.
In particular, the AllNoun project developed a grammer composed entirely of nouns (plus 4 punctuation symbols, which is fewer than the number of punctuation symbols in most languages).
Other conlangers have attempted to eliminate all nouns. One approach is to replace nouns with a series of adjectives that modify a pronoun, similar to the way Toki Pona expresses the noun "soldier" with "jan utala" (literally "fighting person") from jan (person) utala (fight) or the proper noun "Lisa" with "jan Lisa" (literally "Lisa person").
- Tom Breton. "AllNoun: Grammar with only one part of speech." 1995.