Work item link: Blocked and Depend on

There is no built in behavior or semantic implemented. The link is pretty much only information.
If you want to change that, you would have to implement a precondition aka an advisor that checks during the work item save condition, if the save can run (based on the existence of such relationships) and prevent it if not.

 Here is an example based on other information: https://rsjazz.wordpress.com/2014/05/26/only-owner-can-close-workitem-advisor/

The blog provides more reading and also examples how to detect relationships on work items. Note, this is not a cheap endeavor.