“righteousness.” In this context, “righteousness” is doing what is right to God and others (see commentary on Matt. 5:6).
“fall by it.” That is, fall to his death, or die unsaved.
“live by it.” This is the “pregnant sense” of “live,” where it refers to staying alive with God’s blessing but more fully refers to living forever. Thus, the primary meaning of “live” here is “live forever.” In the Church Age, believers are “born again,” which is a one-time event of spiritual birth that assures that they will live forever. However, before the Day of Pentecost, in the Old Testament and Gospels, a person had to maintain their trust in God to be assured of being saved. [For more on the permanence of Christian salvation, see Appendix 1, “The Permanence of Christian Salvation”].