  A recent work by Lesnick and Wright proposed a visualisation of $2$D
persistence modules by using their restrictions onto lines, giving a family of
$1$D persistence modules. We give a constructive proof that any $1$D
persistence module with finite support can be found as a restriction of some
indecomposable $2$D persistence module with finite support. As consequences of
our construction, we are able to exhibit indecomposable $2$D persistence
modules whose support has holes as well as an indecomposable $2$D persistence
module containing all $1$D persistence modules with finite support as line
restrictions. Finally, we also show that any finite-rectangle-decomposable $n$D
persistence module can be found as a restriction of some indecomposable
$(n+1)$D persistence module.
