let $L_c$ be the class of all languages that have a polynomial reduction to some language L, for example if $L=SAT$ then $SAT_c=NP$.
Assuming know that $NP\neq P$ we know that there exist languages that are not NP-hard and not in P, i.e. those in NPI. My question is there a language L in NPI such that $L_c \setminus \{L\}=P$?