Traditional Legal Model – some define a breach as God’s action to punish sin. Examples:
“breach—the calamity wherewith God visited Israel for their sin” (Jamieson-Fausset-Brown Bible Commentary)
“The repairer of the breach: breach is put here collectively for breaches, which were made by God’s judgment breaking in upon them in suffering the walls of their towns and cities to be demolished, and their state broken, Isaiah 5:5.” (Matthew Poole’s Commentary)
Biblical Healing Model – breaches are the actions of man breaking God’s law and the results of those actions (so both a verb and noun). Breaches can, ultimately, include broken relationships.
Dictionary definitions do not vary significantly between modern ones and Webster’s 1828 dictionary.
Aside from physical breaches (as in a wall or defense), a breach can be of a law as this verse shows:
“Wherefore thus saith the Holy One of Israel, Because ye despise this word, and trust in oppression and perverseness, and stay thereon: Therefore this iniquity shall be to you as a breach ready to fall, swelling out in a high wall, whose breaking cometh suddenly at an instant.” (Isa 30:12-13)
The iniquity is seen as a breach or the breaking of a law. A breach is also the result, the damage, the breaching of a defense, the hole in the wall, etc.
Please see this page for an important explanation of a breach in relation to God’s law.
As explained in that link, a sin is a breach of the law and leads to what? God actively punishing the sin? No. Rather, it leads to breaches in God’s wall of protection leaving the sinner subject to the natural consequences of his actions and even the attack of Satan.
“A wholesome tongue is a tree of life: but perverseness therein is a breach (H7667) in the spirit.” (Pro 15:4)
“Your sin in rebelling against God, rejecting the warnings of his prophets, and trusting in your own devices shall bring you into the condition of a wall in which there is a ‘breach,'” (Pulpit Commentary)
A breach can also cause an injury to a person or group of people:
“What thing shall I take to witness for thee? what thing shall I liken to thee, O daughter of Jerusalem? what shall I equal to thee, that I may comfort thee, O virgin daughter of Zion? for thy breach is great like the sea: who can heal thee?” (Lam 2:13)
“Therefore thou shalt say this word unto them; Let mine eyes run down with tears night and day, and let them not cease: for the virgin daughter of my people is broken with a great breach, with a very grievous blow.” (Jer 14:17)
“Moreover the light of the moon shall be as the light of the sun, and the light of the sun shall be sevenfold, as the light of seven days, in the day that the LORD bindeth up the breach of his people, and healeth the stroke of their wound.” (Isa 30:26)
“Breach for breach, eye for eye, tooth for tooth: as he hath caused a blemish in a man, so shall it be done to him again.” (Lev 24:20)
“And the people repented them for Benjamin, because that the LORD had made a breach in the tribes of Israel.” (Jud 21:15)
Why a breach in the tribes of Israel? Because the tribe of Benjamin was virtually wiped out. Who did that? God or the other 11 tribes? While the verse above can make it seem that God did it, other verses show the almost-genocide of the tribe was by the action of the other eleven tribes. – Judges 20:35, 48
This must be understood in terms of the common practice of Bible writers ascribing to God responsibility for the actions of man.
For an example of man causing a breach in the law and how it (not God) caused the death of one involved in that breach read The Breach of Uzzah.
Please read an explanation of the phrase “repairer of the breach” as in the following verse to see that it is referring to more than how we commonly think of sin against God’s law.
“And they that shall be of thee shall build the old waste places: thou shalt raise up the foundations of many generations; and thou shalt be called, The repairer of the breach, The restorer of paths to dwell in.” (Isa 58:12)