Essentially, Irrational Games is no more , but that doesn't mean the revered Bioshock franchise will disappear.
Publisher 2K Games isn't that stupid. Anybody with a brain assumed 2K would bring the Bioshock IP to another capable developer at some point and clearly, that's what they intend to do. Here's a statement 2K gave GameSpot :
"The BioShock universe remains a rich creative canvas for many untold stories, and we look forward to exploring the next BioShock experience."
Creator Ken Levine has formed a "smaller, more entrepreneurial" team at Take-Two, but he wanted to move on. As for his future projects, or if he'll have a hand in designing future Bioshock entries, that's all unknown at this point. He's just so important to the industry; we just want to see what he creates next. Here's the rest of the publisher's statement:
"BioShock is one of our most beloved and critically acclaimed franchises, and we are indebted to Ken and the talented team at Irrational Games for their contributions to the series with BioShock and BioShock Infinite; the latter being one of the most decorated games of 2013."