A brief review of searches for eta-mesic nuclei is presented with emphasis on photoreactions and results of a new experiment done at the LPI electron synchrotron are reported. Decay products of eta-mesic nuclei presumably formed by photons in a carbon target, namely correlated back-to-back (pi+ n) and (p n) pairs, have been studied with a two-arm time-of-flight setup. The obtained data show that apart from previously observed (pi+ n) pairs from one-nucleon annihilation of stopped etas (via eta N --> pi N) correlated (p n) pairs from two-nucleon absorption of eta in the nucleus (via eta NN --> NN) are also ejected with a comparable rate. The cross section of eta-mesic nuclei photoproduction off carbon was estimated from the obtained data to be less than 10 microbarn.