kaku
1.

To damage or impair a solid object, making it incomplete or less functional.

2.

To lack an essential quality or characteristic, resulting in an inadequate state.

3.

To remove a portion of a larger item through breaking or fragmentation.

4.

To neglect a responsibility or duty, leading to a deficiency in one's actions or obligations.

Example:

彼は人間としての感情を欠いていた。

ことか事欠kotokaku
1.

To find oneself in a situation where essential resources or elements are unavailable, causing difficulties in fulfilling a task or need.

2.

To make an inappropriate choice or take an undesirable action when more suitable options exist, often implying poor judgment in the decision-making process.

Example:

彼は贅沢品は言うまでもなく、日用品を買うのにも事欠く。