I think the chance that this happens is very low, it is almost impossible.
Try to imagine, if the price of 1 satoshi is $ 1, the Bitcoin will cost $ 100 million. It is a terrible figure, it's too big.
Currently the price of Bitcoin is about $ 1,170, so if you have $ 1, you will have 100000 satoshi. This shows that the price of 1 satoshi is $ 1 will be very unlikely. The value of Bitcoin is growing very fast, it is very developed but it remains at a certain level.
If this happens I think there will be many people become millionaires because many people have more than 1BTC and the world economy will be able to big changes and that fact is almost impossible.
True, it is impossible for satoshi to become same value as dollar. I can't imagine,if that happens Bitcoin will become 100 000 000 and many bitcoin users will become billionaire. I think that might not happen because its too big, anyone can be rich in a such time through faucets. And it's unfair for those people who used bitcoin for a long time, they work hard inorder to gain bitcoin.