While iOS 7.1 and 7.1.1 were certainly negative blows to the jailbreak community, effectively patching the UnTethered evasi0n jailbreak utility, we continue to receive and answer questions related to whether it’s possible to jailbreak 7.1.1 Untethered.

https://www.jailbreakevasioninfo.com/jailbreak-ios-7.1.1-pre-cydia-tweak-multi-window-functionality/