Feature removal from computational geometries, or defeaturing, is an integral part of industrial simulation pipelines. Defeaturing simplifies the otherwise costly or even impossible meshing process, speeds up the simulation, and lowers its memory footprint. Current defeaturing operators are often based on heuristic criteria and ignore the impact of the simplifications on the PDE solution. This work extends the mathematically rigorous framework developed in [5] to features subject to Dirichlet boundary conditions in Poisson problems. We derive a posteriori error estimators for negative features in the interior or on the boundary of the computational domain. The estimators' dependence on the feature size is explicit, and their evaluation only involves boundary integrals over the feature boundary. Numerical experiments in two and three dimensions showcase the validity and efficiency of the estimators.