to enrich oneself when an opportunity occurs is correct because feather one's nest means to make oneself richer or more comfortable, often by taking advantage of a position or opportunity.

This idiom or phrase is useful because it helps students understand the intended meaning beyond the individual words.

Examples: The corrupt officer used public money to feather his own nest. Some leaders care more about feathering their nest than helping the people.

The idiom is figurative; it is not about birds, nests, or literally building a house.