“How long can you live without a liver?”

I am assuming you are scheduled for a living donor liver transplant. No liver function at all is incompatible with life. Liver transplant is performed when there is still residual function. Allocation of deceased donor livers follow a score named MELD that prioritize the sickest patient. With a MELD of 40 chance of short term survival without liver transplant is limited.

Several days.