Our first goal is always to outright delete negative content, but some websites have policies to never remove content. In these situations, our team will fight to have the content deindexed.
When something is deindexed, the content still exists, but it has been completely removed from a search engine. It will not be findable on any search term, regardless of what is searched. Generally, deindexing is just as effective a solution as deletion because the only way to find the deindexed content is to go directly to the website it’s hosted on and search for it (which almost never happens in practice and is nearly impossible to find if you already didn’t know that content existed in the first place).