There are two types of project dependencies:Intra-project - Dependent relationships within projects
Inter-project - Dependent relationships across projects
You have the option to notify project owners and task assignees when their parent project or parent task is completed or when date intervals among inter-project dependencies are changed. Go to Account Settings > Notifications to configure.
Basecamp users: Date changes to "parent" work item or project must be made in Roadmap to trigger "child" date changes.