This paper presents a complete solution to the problem of comprehensive admissibility for descriptor systems with unstable and nonproper weights. In such non-standard circumstances, it is hard to render the closed-loop system admissible due to the uncontrollable and unobservable weights. The necessary and sufficient condition is given and a specifically structured output feedback controller is conducted in terms of the dynamics of the weighs. It is shown that determining suitable controllers for a given descriptor system with the presence of unstable and nonproper weights requires solving an admissibility problem for an augmented system explicitly constructed in this paper. A numerical example is included to illustrate the current result.