In this paper, we investigate the information-theoretic secrecy performance of recent precoded faster-than-Nyquist signaling (FTN) with the aid of optimal power allocation in eigenspace. More specifically, the secrecy rate and secrecy outage probability of a fading wiretap channel, which was derived for classical Nyquist-based orthogonal signaling transmission, is extended to those of our eigendecompsition-based FTN (E-FTN) signaling for a quasi-static frequency-flat Rayleigh fading channel. Our performance results demonstrate that the proposed E-FTN signaling scheme exhibits improvements in secrecy rate and secrecy outage probability over conventional Nyquist-based and FTN signaling transmission, assuming employment of a root-raised cosine filter. We also show that the same benefits as those of single-carrier E-FTN signaling are attainable by its non-orthogonal multicarrier counterpart, where subcarrier spacing is set lower than that of orthogonal frequency-division multiplexing.