The line "'Cause there's no one left to finger" is followed by "there's no one here to blame". She's not talking about fingering anyone... she's saying that there is no one else to point a finger at - she can't blame anyone.
The line "'Cause there's no one left to finger" is followed by "there's no one here to blame". She's not talking about fingering anyone... she's saying that there is no one else to point a finger at - she can't blame anyone.