I've noticed that. The sensor plug in above the oil filter on my camaro is gone. What type of problem could occur or has already has occurred due to it's absence.

What do you mean gone? Do you mean it fell out and the oil is coming out or do you mean it is broke and a portion fell off but the block is still plugged (no leaks) or what?

The mear absense of an indication of oil pressure will only illuminate an idiot light or not read on a pressure gauge and will not damage your engine. You are just left in the dark about oil pressure? But, if it came out and caused your oil galley to be pumped dry......different story. It could be damaged and then again maybe not depending on how far it was driven.
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Steve "Jack'Stands" Jack