Can someone explain the logic of trying to keep someone alive after a botched execution?

I forgot what state it happened in, but it's all over the news. Some lady was scheduled to be executed today for a murder she committed THREE DECADES ago! Anyways, they injected her with the stuff TWICE and she ended up just snoring and passing out and making some noises, and didn't die. But the poison is still inside her, and now she's been taken to the hospital where the prison staff instructed the doctors to "save her life", even though the State wants her DEAD. You really can't make this up.

Can someone explain the logic of trying to keep someone alive after a botched execution?
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