A search for Majoron-emitting modes of the neutrinoless double beta decay of Xe136 is performed with the full EXO-200 dataset. This dataset consists of a total Xe136 exposure of 234.1 kg·yr, and includes data with detector upgrades that have improved the energy threshold relative to previous searches. A lower limit of T1/2Xe136>4.3×1024 yr at 90% C.L. on the half-life of the spectral index n=1 Majoron decay was obtained, a factor of 3.6 more stringent than the previous limit from EXO-200 and a factor of 1.6 more stringent than the previous best limit from KamLAND-Zen. This limit corresponds to a constraint on the Majoron-neutrino coupling constant of |geeM|<(0.4-0.9)×10-5. The lower threshold and the additional data taken resulted in a factor 8.4 improvement for the n=7 mode compared to the previous EXO-200 search. This search provides the most stringent limits to date on the Majoron-emitting decays of Xe136 with spectral indices n=1, 2, 3, and 7.

A search for instability of nucleons bound in Xe136 nuclei is reported with 223 kg·yr exposure of Xe136 in the EXO-200 experiment. Lifetime limits of 3.3×1023 and 1.9×1023 yr are established for nucleon decay to Sb133 and Te133, respectively. These are the most stringent to date, exceeding the prior decay limits by a factor of 9 and 7, respectively.