We employ molecular dynamics (MD) simulations to study the spreading and imbibition of a liquid drop on a porous, soft, solvophilic, and responsive surface represented by a layer of polymer molecules grafted on a solvophilic solid. These polymer molecules are in a crumpled and collapsed globule-like state before the interaction with the drop but transition to a "brush"-like state as they get wetted by the liquid drop. We hypothesize that for a wide range of densities of polymer grafting (sigma(g)), the drop spreading is dictated by the balance of the driving inertial pressure and balancing viscoelastic dissipation (associated with the spreading of the liquid drop on the polymer layer that undergoes globule-to-brush transition and serves as the viscoelastic solid). Using the well-known idea that the viscoelastic resisting force exerted by the viscoelastic solid on a spreading drop scales as u(n) (where n is the index of the power-law-like rheology of the polymer layer serving as the viscoelastic solid and u is the spreading velocity of the drop on this viscoelastic solid) and considering n = 2/3, we show that the scaling calculation recovers the MD simulation prediction of r similar to t(1/4) and req similar to sigma(-1/3)(g) (where r and r(eq) are the instantaneous and equilibrium spreading radii, respectively). We further describe the wicking behavior of the drop through the polymer layer by appropriately accounting for the manner in which the progressive time-dependent swelling of the grafted polymer molecules provides larger space for the wicking. Third, we quantify, possibly for the first time, the temporal dynamics of the "brush"-forming process (i.e., capture the dynamics of wetting-mediated globule-to-brush transition). We show that the dynamics of the polymer chain swelling depends on sigma(g) and is faster for sparser grafting. Most importantly, we confirm that the height of the relaxed polymer chains approximately scales as sigma(1/3)(g), confirming the attainment of brush-like configuration by the polymer molecules as they are wetted by the liquid drop. Finally, we argue that our simulations raise the possibility of designing soft, "responsive", and widely deployable liquid-infused surfaces where the polymer grafted solid, with the polymer undergoing a globule-to-brush transition, serves as the responsive "surface".