  Prefix normal words are binary words in which each prefix has at least the
same number of $\so$s as any factor of the same length. Firstly introduced by
Fici and Lipt\'ak in 2011, the problem of determining the index of the prefix
equivalence relation is still open. In this paper, we investigate two aspects
of the problem, namely prefix normal palindromes and so-called collapsing words
(extending the notion of critical words). We prove characterizations for both
the palindromes and the collapsing words and show their connection. Based on
this, we show that still open problems regarding prefix normal words can be
split into certain subproblems.
