  We define the finite extension property for $d$-dimensional subshifts, which
generalizes the topological strong spatial mixing condition defined by
Brice\~no (2016), and we prove that this property is invariant under
topological conjugacy. Moreover, we prove that for every $d$, every
$d$-dimensional block gluing subshift factors onto every $d$-dimensional
subshift which has strictly lower entropy, a fixed point, and the finite
extension property. This result extends a theorem from Boyle, Pavlov, and
Schraudner (2010), which requires that the factor contain a safe symbol.
