Semi-Lagrangian schemes have gained prominence in recent years for the numerical resolution of hyperbolic conservation laws, kinetic equations, fluid dynamics, and other applications. One for the main reason for their success lies in their excellent stability properties (they are not subject to the CFL condition, allowing the time step to be chosen larger compared to direct mesh-based methods). However, these methods are not conservative, and the preservation of invariants or positivity of the solution are not guaranteed. Positivity can be physically significant for certain applications, especially in the resolution of kinetic equations, where the solution represents a probability density that must inherently be positive. In this talk I will investigate the reasons why this property cannot always be ensured and how it can instead be enforced when solving the BGK equation, using some techniques applied recently for Runge Kutta IMEX schemes, while maintaining high order of accuracy and moment conservation.