Fluid reconfigurable intelligent surfaces (FRIS) extend conventional RIS architectures by enabling physical reconfiguration of element positions, thereby introducing a fundamentally new degree of freedom for controlling spatial correlation and improving link reliability. Despite this promise, rigorous performance analysis of FRIS-assisted wireless systems has remained challenging, as exact statistical analyses of the end-to-end cascaded channels have been unavailable. This paper addresses this gap by providing the first exact closed-form characterization of the end-to-end cascaded channel gain in FRIS-aided systems under general spatial correlation. By exploiting the spectral structure of the FRIS-induced correlation matrix, we show that the channel gain statistics can be represented as a finite linear combination of K-distributions. This unified formulation naturally captures fully correlated, effectively decorrelated, and intrinsically uncorrelated operating regimes as special cases. Building on the derived channel statistics, we further obtain exact closed-form expressions for the outage probability and ergodic capacity. We also conduct an outage-based asymptotic analysis, which reveals the true diversity order of the system. Numerical results corroborate the proposed analytical framework via Monte Carlo simulations, benchmark its accuracy against state-of-the-art approximation-based approaches, and demonstrate that fluidic reconfiguration can yield tangible reliability gains by reshaping the spatial correlation structure.