In this study, we achieve this remarkable feat: we are able to enforce controlled and complete de-encapsulation of magnetic nanoparticles (in the form of nanoaggregates) from the interior of a MNLD. Specifically, we achieve the de-encapsulation of the polyvinylpyrrolidone(PVP)-coated Fe3O4 NPs. We start with such PVP-coated Fe3O4 NPs dispersed in an aqueous drop that is inserted into a partially uncured polymer medium, i.e., polydimethylsiloxane (PDMS). On subjecting the MNLD to a non-linear strong magnetic field (i.e. max magnetic field strength of ~0.2 mT), we observe that (1) the drop moves in the direction of increasing magnetic field, (2) aggregation of MNPs occur within the drop at the drop-PDMS interface (in the direction of the applied magnetic field) leading to a sub-millimetric sized aggregate, (3) subsequent complete de-encapsulation of this aggregate from the interior of the drop, and (4) the drop returning back to its previous spherical shape. The de-encapsulation is characterized by (1) the distance from the magnet at which the de-encapsulation of the aggregate occurs (this distance is denoted as the de-encapsulation distance, or hde) and (2) the volume of the de-encapsulated aggregate (Vagg). We characterize the de-encapsulation phenomenon by quantifying hde and Vagg as functions of the drop volume (Vd) and the concentration of the magnetic NPs (cMNP) inside the drop. The underlying key to this phenomenon is ensuring that the aggregate (inside the drop) is subjected to the magnetic field (that varies inversely as hde) that ensures a magnetic force (that scales Vagg) that is large enough to overcome the resisting water-PDMS capillary force (that scale as the length of the aggregate). We develop a theoretical model that accounts for these physical factors and the resulting theoretical prediction matches well with the experimental trends. We anticipate that this technique of achieving the complete de-encapsulation of NP aggregates from the drop interior that has been introduced here will be matured further in near future enabling de-encapsulation of other types of particles in less viscous media (such as air or oil), thereby providing pathways to wide-ranging applications (e.g., 3D printing) that rely on the "on-demand" and controllable particle deposition at desired locations and in desired amounts.