The dissolution of Ammonium chloride in water is endothermic, but still it dissolves in water.
Whether or not the heat of solution is an endothermic or an exothermic process depends on the relative magnitude of the lattice energy and the heat of salvation. If tearing the ions apart requires more energy than is released by salvation, then D Hsoln is going to be positive (endothermic). If the energy released by salvation is greater than the energy required to tear the ions apart, D Hsoln is going to be exothermic.
However, Solubility of a compound does not depend whether it is an exothermic or endothermic reaction in water. NH4Cl is an electrolyte and dissociates in water as NH4+ and Cl- ions to form NH4OH and HCl which immediately combine to form NH4Cl. It is a reversible reaction.