* Metal debris: Without oil, engine parts will grind against each other, creating metal shavings and debris. This debris can circulate through the engine's oil passages and eventually reach the fuel injectors. The debris can clog the fuel injectors or scratch their delicate internal components.
* Increased engine temperature: The lack of lubrication leads to extreme heat build-up. This intense heat can damage the fuel injectors themselves, potentially warping or melting internal parts. The extreme heat can also cause the fuel to vaporize, leading to erratic injector operation.
* Hydrolock (in some cases): If the engine seizes completely, it may cause the connecting rods or pistons to deform, possibly leading to coolant, or even oil, mixing with the fuel system causing problems for the injectors. While this might not be solely a fuel injector problem, it further complicates things.
While the fuel injectors themselves aren't directly lubricated by engine oil, the *consequences* of running an engine without oil will almost certainly lead to their failure or malfunction. It's much more likely that the entire engine will require a rebuild or replacement, making the cost of replacing the fuel injectors a small fraction of the total repair bill.