pick up the slack

伊坂幸太郎氏の小説 "Remote Control" を読んでいます。パート4，The Incidentから引用します。

"Can't say I blame you," Aoyagi said. Kazu was as idealistic as he'd been back in school.
"So I quit. I wanted them to see how much they needed me, how hard it would be if I wasn't there to pick up the slack."
"And did they see the error or their ways?"

"pick up the slack" の意味を調べます。

・Collins COBUILD Idioms Dictionary: If someone or something takes up the slack or picks up the slack, they reduce the bad effect of something by providing something extra. With the export market in decline, it is hoped that the tourist trade will take up the slack. We have three members of staff absent and no one to pick up the slack.
・Farlex Dictionary of Idioms: To do an extra amount of work that someone else is unable or unwilling to do.: The fourth member of our team has been totally unreliable, so the rest of us have had to pick up the slack.
・Merriam-Webster: to provide or do something that is missing or not getting done: When he didn't get the pay raise he was expecting, he had to take another job to pick up the slack for more money.

代わりをするとか補うの意味ですね。たるみを直すことから来ている様です。
Vocabulary.comのslackの説明にこの "pick up the slack" が出てきます。
If you slow down at the end of a race, you slack off. When you use slack this way, it means to reduce your speed, to be sluggish, or to be negligent.
If something is loose, it's also said to be slack. A clothesline, for example, is slack if it is just hanging loosely between two trees. If you pull the clothesline tight, you reduce the slack. The root word of slack is the Old English word slæc, which means "loose or careless." When you scold your friend for being careless about his responsibilities, you can say, "Pick up the slack!"