what is an open configuration?

It means there is no conductivity through the remains of the resistor. As if someone had cut the wire or opened a toggle switch.

This is opposed to failing in a closed configuration as in some semiconductors. This is as if there were a short or low resistance wire in place of the device.

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Open circuit.

Infinite resistance.

No current flow.

To "fail in an open configuration" means it burned out and the connection through it is open, not connected, infinite resistance. Burned open like a fuse.

In other words: "When a resistor fails, it no longer conducts at all, as if it isn't there, completely open."