Cells must be alive to use energy and do work dose passive transport occur in a cell that is dead? Why or why not?

Yes, Passive transport can occur in dead cells.

Explanation:

For passive transport to occur, a concentration gradient has to be formed across a permeable or semi-permeable membrane. If the cell membrane of the dead cell, which is a semipermeable membrane, is intact and a concentration gradient has formed on both sides, passive transport can occur.

A concentration gradient is the difference in the concentration of solute molecules across the membrane. Passive transport will allow solute molecules to travel from the higher concentration of the solute to the lower concentration across a membrane till equilibrium is reached, that is, both the sides of the membrane has equal concentration of the solute.

The transport of the solvent can occur as well, from higher concentration to lower concentration.