Warning: SPOILERS for The Walking Dead season 10, episode 12.
In Carol's journey on The Walking Dead has certainly been an interesting one, and it was only when she was with Ezekiel and Henry that she allowed herself to feel happy.
Once everything was taken away from her, she put everyone else in danger by being consumed by her quest to kill Alpha. So when Negan escaping was all part of Carol's plan.
It seems that in The Walking Dead season 10, episode 4, "Silence the Whisperers", Carol let Negan out and gave him a path to redemption: kill Alpha and deliver her head to Carol. He did just that in "Walk With Us" by luring Alpha to a shack that he pretended to have Lydia held up inside. Getting her there took time and a lot of convincing on his part; he had to, essentially, the Whisperers by helping them in their attack on Hilltop.
Negan has been trying to prove that he's not the person he once was. While he may fondly being in charge of an organization like the Saviors, he doesn't seem to miss killing people. He even tried to save the mother and son that Brandon killed. But in order for everyone else to believe he's changed, he needed to convince someone like Carol who re fighting him and the Saviors all those years ago. And Carol knew he was the right person for the job, considering his charm.
Carol had a multi-pronged plan: have Negan infiltrate the Whisperers and kill Alpha while she searches for the horde with some of Alexandria and Hilltop. It would've been a clean way to defeat the Whisperers from the inside out - but while one part of the plan worked without a hitch, the other part resulted in multiple casualties. A lot of people almost died in Alpha's cave, but most of them got out. Magna has since returned, but Connie is still missing - and it may be a while before she reappears.
Even from the beginning, The Walking Dead comics and TV show have been different, both following the same rough path but getting there in alternate ways. Negan kills Alpha in the comics, but in the TV series, he does it for Carol, who charged him with the task. What happens after this - if Negan is accepted by the survivors and not jailed once again - remains to be seen, but for now, Carol's plan to get revenge on Alpha while simultaneously disrupting the Whisperers from within has succeeded.