Some modern translations will replace the last phrase with something akin to "nothing can make them stumble." Nothing can entice them to sin, nor can the sins of others cause them to fall.
As a fruit, the love of God's instruction—paying attention to and keeping His law—produces peace, which is a wonderful, strong sense of well-being, stability, and confident assurance in what we already have. Thus, the enticement to go another way holds no attraction. Why exchange something we have proven to be eternally good for something else of very nebulous and doubtful short-term value?
The psalmist writes in verse 49, "Remember the word to your servant, upon which You have caused me to hope." Why turn aside from a way that gives hope? "This is my comfort in my affliction, for Your word has given me life. . . . I am a companion of all those who fear You, and of those who keep Your precepts" (verses 50, 63). Peace, hope, comfort in affliction, fellowship with wonderful, like-minded people also submitting to God, and life all come as a result of loving God's law. In other verses, he adds delight, understanding, and wisdom.