Time-resolved x-ray emission/absorption spectroscopy (Tr-XES/XAS) is an informative experimental tool sensitive to electronic dynamics in materials, widely exploited in diverse research fields. Typically, Tr-XES/XAS requires x-ray pulses with both a narrow bandwidth and subpicosecond pulse duration, a combination that in principle finds its optimum with Fourier transform-limited pulses. In this work, we explore an alternative experimental approach, capable of simultaneously retrieving information about unoccupied (XAS) and occupied (XES) states from the stochastic fluctuations of broadband extreme ultraviolet pulses of a free electron laser. We used this method, in combination with singular-value decomposition and Tikhonov regularization procedures, to determine the XAS/XES response from a crystalline silicon sample at the L_2,3 edge, with an energy resolution of a few tens of meV. Finally, we combined this spectroscopic method with a pump-probe approach to measure structural and electronic dynamics of a silicon membrane. Tr-XAS/XES data obtained after photoexcitation with an optical laser pulse at 390 nm allowed us to observe perturbations of the band structure, which are compatible with the formation of the predicted precursor state of a nonthermal solid-liquid phase transition associated with a bond softening phenomenon.