Point-gap bound states in non-Hermitian systems are generally expected to lose their purely impurity-localized character under open boundary conditions (OBC) owing to hybridization with the non-Hermitian skin effect (NHSE). Here, we demonstrate that such states can retain impurity localization in a one-dimensional non-Hermitian continuum, even after point-gap collapse under OBC. The mechanism is a non-Bloch standing wave established between the impurity and a boundary, which suppresses the skin-accumulating components. Experimentally, we use a programmable piezoelectric actuator array mounted on an elastic beam to introduce non-Hermiticity and directly observe the predicted OBC-persistent point-gap bound state. Our results establish a route for preserving impurity localization against NHSE hybridization.