Exposed cord on bike tire - replace?
Definitely replace it.

At this stage, with the rubber delaminating from the case, it could come apart at any time. It's dangerous to use. 

Near the bottom of the picture there are some bare threads. It is at that point the tire should have been replaced and perhaps only used in an emergency.

PS I see from the picture that the rim is quite worn. It's not far off needing replacement also.