If I jailbreak my iPhone 4 5.1.1 can I let it die?

People say if it dies it won't turn back on is this true

No Period.

NO it won't die since 5.1.1 is untethered
follow this link:- http://www.redmondpie.com/jailbreak-ios-5.1.1-untethered-using-redsn0w-0.9.12b1/

Jailbreak using Absinthe 2.0.4 from http://greenpois0n.com/.
Absinthe is the untethered jailbreak software created along with "Rocky Raccoon Untether," the Cydia tweak.

If you do untethered jailbreak, it's completely okay to let it turn off. It will turn on again.

If you have done tethered jailbreak (with Redsn0w), you'll have to download Rocky Racconn from Cydia.

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