Yes; one of the executor's jobs is to pay the deceased's "final expenses," which includes burial and/or cremation. However, the executor is not personally responsible or liable for these expenses; he or she pays them out of the estate's money, not his or her own, and does not need to pay them out of his/her pocket even if the estate has insufficient money for the burial (unless, that is, that the executor *knew* or should have known there was not enough money at the time he/she hired the funeral home, bought the plot, etc.--in that case, it is possible that the executor could be personally liable, such as for fraud).