To be Nibbled To Death means that you've been charged for this, charged for that, charged for every little thing, and while each charge on its own may have been insignificant, the totality is overwhelming.
Banks in the UK excel at this.
The phrase often heard in the U.S. is actually "Nibbled to Death by Ducks" ... Same phrase?
I believe here in the UK it's more recognisable as what happens to students. ;-)
Actually, in The Good Ol' US of A we say, "Nickel and dimed to death," meaning small charges applied all over the place that add up to a large drain on finances. - Indeed, if you click on the title of this page you'll find it referenced by NickelAndDime.
Charge'em for the lice Extra for the mice Two percent for looking in the mirror twice. Here a little slice There a little cut Three percent for sleeping with the window shut. When it comes to fixing prices There are lots of tricks he knows How it all increases All those bits and pieces - Jesus! It's amazing how it grows.
Google sez:
A particular form of "death by a thousand cuts".