Microsoft announced Chaseable Live Tiles here at Build 2016 today.
The new option for developers gives a smarter Live Tile ability where the story listed on the Live Tile is the first story in the app itself. In other words, the Live Tile and ordering of stories or targets within the app will all be synced together.
The feature is a rather simple addition but delivers a consistent user experience if implemented. What the user sees on the Live Tile is the first thing they see in the app when they 'chase' the link.
No word yet when the feature will be delivered to developers but presumably it will come with the Anniversary update to Windows 10 and Mobile due later this summer.
Microsoft has been 'prototyping' so-called interactive Live Tiles for a long time, but "trying to get it right" before committing. Currently, there is nothing new to announce there yet, but it is something they are interested in doing.
Update: Here's the video of the session: