I agree with Tom.
Unless you are a demon chain-and-sprocket cleaner,
your chain has needed lubrication for a long time.
I spray my chain liberally (but not generously) every 500 miles,
and clean it with kerosene every 5000 miles or so, or just before
a long trip. You can find lots of info on chain maintenance here.
And no, do not ride an inch until you get a new rear sprocket.
I cannot understand how your chain and front sprocket can be OK
when there is such catastrophic damage to the rear sprocket.
Please get a pro to examine those components before riding.
My first chain and sprockets lasted 22000 miles, and so did my second.
With my third chain and third front sprocket, I re-used a rear sprocket,
but that rear sprocket is mounted backward, with five washers to
align it properly with the front sprocket. All is well, and I definitely do
not see any increased chain wear or any other symptoms of trouble.
I have run 18000 miles this way, and the chain will likely last another
four thousand miles, then it will be time for another front sprocket,
another chain, and reverse mounting of the original rear sprocket.
I get my sprockets from my friendly local Suzuki Dealer, here in Sarasota.
I buy chain lubricant from any bike shop, most recently from a Harley store.
By the way, if your handle means you are a Canadian, you are not alone.
So am I.