Given a set S of morphisms, an infinite word is limit S-adic if it can be recursively desubstituted using morphisms in S. Substitutiveadicity arises naturally in various studies especially in studies on infinite words with factor complexity bounded by an affine function. In the literature, when a family F of infinite words defined by a combinatorial property P appears to be S-adic for some set S of morphisms, it is very rare that the whole set of limit S-adic words coincides with F . The aim of the talk is to survey such situations in which necessarily morphisms of S preserve the property P of infinite words.