We report tailed skyrmions—a new class of stable soliton solutions of the 2D chiral magnet model. Tailed skyrmions have elongated shapes and emerge in a narrow range of fields near the transition between the spin spirals and the saturated state. We analyze the stability range of these solutions in terms of external magnetic field and magnetocrystalline anisotropy. We calculate minimum energy paths and homotopies (continuous transitions) between tailed skyrmions of the same topological charge. The discovery of tailed skyrmions extends the diversity of already known solutions. This is illustrated by solitons with complex morphology, such as tailed skyrmion bags with and without chiral kinks.