Taking NuGet as an example - you make a change, bump the version number, commit and push it. The buildserver automatically push it to your internal NuGet server. Now your IDE will notify you that there is an update to a package you use and you can update and make your own bugfix, and commit it.

The alternative with monorepo is - you make a change, bump the version number, commit and push it. You watch for the commit you need (in a monorepo this might be harder than it have to be, alternatively the developer can send you an IM) and hopefully there isn't any merge conflicts when it's done. You pull the commit, make your fix and commit it.

It's largely a matter of poor tooling.