The 'moral fibre' of a person refers to a person's strength of character or the ability of an individual to do what they think is morally right.

1. The politician claimed that the new drug laws will have a negative impact on the moral fibre of society.
2. Brian showed his moral fibre by owning up to his mistake rather than letting someone else take the blame.

1. I could never do business with someone like Kevin. The man is severely lacking in moral fibre so cannot be trusted.
2. My moral fibre prompted me to reveal the shady and underhand dealings within the police force I was working in.