Quick answer
Patience gets further with powerful people than pressure does, and the second line puts it as a paradox: soft speech breaks bone.
Read both lines
The first line is practical counsel about power, and the phrase behind "long forbearance" is literally length of nose, the Hebrew idiom for slowness to anger. So the persuasion in view is not clever argument; it is the sustained refusal to become heated, applied to someone who cannot be pushed.
Then the second line states the same thing as an impossibility. A soft tongue against bone should lose, and the verse says it wins. The image is not violence but attrition, the way water gets through stone, and it explains why the first line works. Nothing in this saying suggests manipulation. It observes that hardness meets hardness and stops, and that the thing which eventually moves an immovable person is usually the thing that never escalated.
Related: Proverbs 15:1 · Proverbs 16:32 · Proverbs 16:14 · Proverbs 24:5–6
New King James Version®, Copyright © 1982, Thomas Nelson. All rights reserved. Full copyright information. Scripture provided by API.Bible.
Go Deeper
If this verse has been used to put weight on you that it was never carrying, ask about it directly.