Continuously ringing means the network still thinks the phone's on the network. When you power down your phone it sends a signal to the network saying it's going off. If you just pull the battery or something else where it doesn't send that signal, the network still assumes (maybe only for a time) that the phone is still on but isn't connected to a tower.
But the ringing only starts once the target phone responds to the paging from network, otherwise the network just keeps on searching and after a timeout informs that the target phone is unreachable or out of coverage area.
That's not true. There are cases (e.g. if the phone was last registered on an overseas network because the person was traveling internationally) where the network will generate a "ring" while still searching for the phone.
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