If the 80 ohm resistor fails, will the 50 ohm and 100 ohm resistor continue to operate? Why or why not?

No, the 50 ohm and 100 ohm resistor will not continue to operate.

Explanation:

A closed circuit is the circuit in which there is no break between the negative and the positive end of the battery.

When in this, combinational circuit the 80 ohm resistor fail then there will not any continue supply of current in the circuit due to the breakage because the electron will flow from negative end of the battery to positive end if their is no breaking in the circuit.

Therefore the 50 ohm and 100 ohm circuit will not continue to operate because of the breaking of the circuit and current will not flow.