  An exact phase-retrievable frame $\{f_{i}\}_{i}^{N}$ for an $n$-dimensional
Hilbert space is a phase-retrievable frame that fails to be phase-retrievable
if any one element is removed from the frame. Such a frame could have different
lengths. We shall prove that for the real Hilbert space case, exact
phase-retrievable frame of length $N$ exists for every $2n-1\leq N\leq
n(n+1)/2$. For arbitrary frames we introduce the concept of redundancy with
respect to its phase-retrievability and the concept of frames with exact
PR-redundancy. We investigate the phase-retrievability by studying its maximal
phase-retrievable subspaces with respect to a given frame which is not
necessarily phase-retrievable. These maximal PR-subspaces could have different
dimensions. We are able to identify the one with the largest dimension, which
can be considered as a generalization of the characterization for
phase-retrievable frames. In the basis case, we prove that if $M$ is a
$k$-dimensional PR-subspace, then $|supp(x)| \geq k$ for every nonzero vector
$x\in M$. Moreover, if $1\leq k< [(n+1)/2]$, then a $k$-dimensional PR-subspace
is maximal if and only if there exists a vector $x\in M$ such that $|supp(x) |
= k$.
