Two-dimensional (2D) membranes consisting of a single layer of Mo atoms were recently manufactured [ Adv. Mater. 2018, 30, 1707281 ] from MoSe2 sheets by sputtering Se atoms using an electron beam in a transmission electron microscope. This is an unexpected result as formation of Mo clusters should energetically be more favorable. To get microscopic insights into the energetics of realistic Mo membranes and nonstoichiometric phases of transition-metal dichalcogenides (TMDs) MaXb, where M = Mo and W and X = S, Se, and Te, we carry out first-principles calculations and demonstrate that the membranes, which can be referred to as metallic quantum dots embedded into a semiconducting matrix, can be stabilized by charge transfer. We also show that an ideal neutral 2D Mo or W sheet is not flat but a corrugated structure, with a square lattice being the lowest-energy configuration. We further demonstrate that several intermediate nonstoichiometric phases of TMDs are possible as they have lower formation energies than pure metal membranes. Among them, the orthorhombic metallic 2D M4X4 phase is particularly stable. Finally, we study the properties of this phase in detail and discuss how it can be manufactured by the top-down approaches.