It is known that microgels can serve as soft, permeable and stimuli-responsive alternative of solid colloidal particles to stabilize oil-water emulsions. The driving force for the adsorption of the microgels on interface of two immiscible liquids is a shielding of unfavorable oil-water contacts by adsorbed subchains, that is, the decrease of the surface tension between the liquids. Such phenomenon usually proceeds if volume fractions of the two liquids are comparable with each other and the microgel concentration is not high enough. The natural question arises: what is going on with the system in the opposite case of strongly asymmetric mixture (one of the liquids (oil) has a very small fraction) or high microgel concentration (the overall volume of the microgels exceeds the volume of the minor oil component)? Here we demonstrate that the microgels uptake the oil whose concentration within the microgels can be orders of magnitude higher than outside, leading to the additional microgel swelling (in comparison with the swelling in water). Thus, the microgels can serve as scavengers and concentrators of liquids dissolved in water. At first glance, this effect seems counterintuitive. However, it has a clear physical reason related to the incompatibility of oil and water. Absorption of the oil by microgels reduces unfavorable oil-water contacts by microgel segments: the microgels have a higher concentration of the segments at the periphery, forming a shell. The microgels with uptaken oil are stable toward aggregation at very small oil concentration in the mixture. However, an increase in the oil concentration can lead to aggregation of the microgels into dimers, trimers, and so on. The increasing concentration of oil mediates the attraction between the microgels: the oil in the aggregates appears to be localized in-between the microgels instead of their interior, which is accompanied by the release of the elastic stress of the microgels. A further increase in the oil concentration results in a growth of the size of the oil droplets between the microgels and the number of the microgels at the droplet's periphery, that is, the emulsion is formed.