It has certainly happened in the past, though not necessarily specifically the narrative part of the game. Many games are pushed to launch without development being as far as they want it to be due to reasons like hitting their budgetary limit and needing to recoup some of the investment. Our estimates are only estimates after all, sometimes we run into unforeseen problems and things take longer than expected. We can't stop paying the developers when we hit snags like that, so certain features end up more costly than others, which eats into the budget that was earmarked for other stuff instead. Most games in this situation have a lot of other launch issues too for the same reason - when you're pushed out the door to make the deadline due to running out of budget, things that should have been fixed are often not.
When World of Warcraft launched in 2004, there were several entire world zones that were incomplete and (mostly) locked off from players. Some players were able to sneak in through various exploits and take screenshots of those areas. Most notable were that the zones were primarily unpopulated by anything - no mobs, no quests, empty towns and buildings, just environment geometry that had been built out. This accompanied other incomplete bits of the game like quests that still had XML code in them. It would take years before players would finally see the incomplete-at-launch zones in some form or other.
Cyberpunk 2077 famously launched after multiple delays with numerous bugs and weird issues. Notably, the dev team also completely cut the multiplayer mode of the game that they had been building in order to consolidate resources to ship the single player game. The game came in super hot and had a huge number of launch issues that were eventually (mostly) ironed out, but the multiplayer mode was never resurrected.
The most famous example of this is probably Knights of the Old Republic 2. The publisher famously moved the deadline up and Obsidian scrapped the in-development ending since they didn't have the time to finish it. Instead, the story was wrapped up super quickly to ship the game. Notably, the partially-finished original ending was left on the disc and modders eventually discovered (and later restored) it.
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