Bungie announced that the Glory system will be revamped in a future Destiny 2 season, which also means you need to working on the Unbroken seal as soon as possible.
Glory has seen its own share of troubles over the years in Destiny 2 and it appears to be the next big revamp in Bungie's sights. When it happens, it will render players unable to gain the Unbroken seal and title, which requires them to earn Legend rank for three seasons in a row.
Due to the Glory changes being planned for Season 19, it means that Season of the Risen (Season 16) is the last one where players can attempt to get the seal and the title.
That said, the top players will still have something to chase after. A new, "similarly challenging", Crucible Seal will be introduced but it will not be a multi-season thing. Bungie will reveal more info on it over the course of the next few seasons.
Before that happens, there will be a new title that will be introduced to Crucible. Based on the pun from the associated TWAB, it's possible it has something to do with wolves or possibly the Iron Lords.
While it makes sense and was probably assumed by many, it's still worth confirming that yes, you will get to keep displaying Unbroken title even after it's retired.
Since Season 19 is the last one in The Witch Queen expansion, it will be fun to see people hunting for the new title with 3.0 Light subclasses as the entire set will be complete by then.