This is something that we try very hard to avoid. All sites are backed up before we manually do any updates, and if your host supports it, a staging version is made as well to test all updates.
If your site breaks due to an update, we’ll first restore a backup to ensure that your customers can still access your site. We’ll then assess the issue and determine why it broke and what it will take to fix. If it was our fault, we’ll fix it for free. If it was a faulty plugin or theme interaction, we’ll determine if it’s an issue that we’re best suited to handle for you.
WordPress and some updates also offer automatic updates. This is often good, especially for security, but would be handled the same way: we’ll determine what it takes to fix and reach out to you before we do anything to your site.