This saying is probably about witnessing in court. The two lines are parallel and are generally taken as a contrast between a false witness and a reliable witness.

“A false witness will perish”: “A false witness” is literally “a witness of lies” and means a person who tells lies in court. “Will perish” is generally taken as the fate or the punishment of the false witness; this makes the line almost identical with the first line of 19.5 and 19.9, which have “will not go unpunished” as the verb. Contemporary English Version renders the whole expression, “If you tell lies in court, you are done for.” But some versions give the verb a different sense, in contrast with the way they understand the matching term “will endure” in the next line. This sense is that the person will not be allowed to speak any more or will not be accepted as a believable witness; for instance, Good News Translation says, “The testimony of a liar is not believed” and Revised English Bible “A lying witness will be cut short.” See the comments on “will endure” below.

“But the word of a man who hears will endure”: The Hebrew of this line is literally “but a man who hears will speak for ever.” New Revised Standard Version renders “a man who hears” as “a good listener”; other versions take the expression either in the sense of someone who has listened carefully and is therefore able to give a truthful testimony (Revised English Bible “a truthful witness,” Contemporary English Version “a reliable witness”), or as meaning someone who thinks about what he or she hears (Good News Translation “someone who thinks matters through”). The last part of the line, “will speak for ever,” may also be understood as “will speak to the end” or “will speak for a long time.” This is seen as a contrast with the “false witness” of the previous line, whose word will be stopped; so Revised English Bible has “. . . will speak on,” New Jerusalem Bible “no one who . . . will ever be silenced,” and New Revised Standard Version “. . . will testify successfully.”

Quoted with permission from Reyburn, William D. and Fry, Euan McG. A Handbook on Proverbs. (UBS Helps for Translators). New York: UBS, 2000. For this and other handbooks for translators see here .