What happens if you charge your iPhone 4 for a week?

I Left my iphone at church and i forgot it there.

Would the iphone it self stop working?

or will the charger stop working?

or will it just stop charging it?

Your iMessage and Facetime will still work, of course but you shouldn't leave your phone charged for a week because it will lessen the life span of your phone's battery. You could just leave your phone alone and it will still get notifications so there's no need to leave it charging because it wouldn't run out of battery while no one is using it.

It will result in a battery leakage or reduced battery life, overcharging a battery is a big no no for your phone, 3 hours max for a charge, depending on battery health

Battery would weaken.

You will lose an iphone. People who finds it would take it away.