There is a lack of knowledge about the composition and particle size distribution of the <80 mm fraction mechanically separated from residual municipal solid waste (rMSW) and the stabilized residual (SR) after aerobic stabilization in a full-scale MBT plant. Therefore, the composition of the particle size fractions (>60 mm, 60–40 mm, 40–10 mm) of the <80 mm fraction and SR, collected in all seasons (summer (S), autumn (A), winter (W), spring (Sp)), was determined. Biodegradable waste (vegetable waste, other organic waste, paper, cardboard) constituted from 44.1% (A) to 54.3% (Sp) of the <80 mm fraction and it decreased to 8.5% (W) to 17.1% (S) in the SR, after effective biodegradation. In SR, the smaller particle size fractions (up to 40 mm) predominated. The main contaminants in SR were plastic, glass, metal, and other waste. Hierarchical clustering indicated that the composition of the particle size fractions of SR was more similar across four seasons than that of the <80 mm fraction. After stabilization and separation, the share of contaminants increased in the SR size fractions, which means that their recovery before landfilling may be profitable. This suggests a new direction in waste management that would be consistent with the principles of a circular economy, in which a waste product, like SR, which previously could only be landfilled, becomes a source of secondary materials.