  In a first time we present a version of the Poincar{\'e}-Lefschetz theorem
for certain cellular cosheaves on a particular subdivision of a CW-complex K.
To that end we construct a cellular sheaf on K whose cohomology with compact
support is isomorphic to the homology of the initial cosheaf. In a second time
we use the first result to generalise the tropical version of the Lefschetz
hyperplane section theorem to singular tropical toric varieties and singular
tropical hypersurfaces.
