牢不可破 is a formal term, most often found in written language, speeches, news reports, and serious discussions. It's less common in casual, everyday chat.
Diplomacy and Politics: This is one of the most common contexts. It is frequently used in official government statements to describe strategic partnerships and alliances that are meant to appear permanent and unshakeable.
Personal Relationships: When used for friendships or family ties, it signifies an extremely deep, loyal, and time-tested bond. You wouldn't use it to describe a friendship of a few months. It's reserved for relationships that have survived significant challenges.
Arguments and Evidence: It can describe logic, evidence, or a legal case that is so well-constructed that it is irrefutable.
Beliefs and Convictions: It's used to characterize someone's unshakeable faith, principles, or even, in a slightly negative sense, their stubborn, old-fashioned ideas.