Existential construction exists cross-linguistically. So a study about existential construction is very important in linguistic studies. In modern Chinese, existential construction and fugitive construction have same sentence structure ‘NL+VP+NP’, and are closely related semantically. Therefore we can recognize it same category. Nevertheless, we can not deny that there is few study about fugitive construction relatively. In this paper, we discussed about fugitive construction, especially means damage. The reason that fugitive construction is important is that fugitive construction of damage meaning belongs to fugitive construction same as general fugitive construction and it has unique characteristics. Fugitive construction of damage meaning shows the progress that a construction creates new constructional ecosystem while it is evolving. We can see productivity and extendability of language through the evolving of ‘NL+VP+NP’ construction from existential construction to fugitive construction to fugitive construction of damage meaning. In addition, fugitive construction of damage meaning is important in understanding the relation fugitive construction and ‘possessor-subject possessee-object’ construction. Fugitive construction of damage meaning has features between general fugitive construction and ‘possessor-subject possessee-object’ construction syntactically. Fugitive construction of damage meaning also plays a intermediate role semantically.