Any special dividends (well anything > 10% of the closing price of a stock) will adjust the contract terms. Nothing to see - move along.
Yes, in the case of a (relatively) low-vol stock like AAPL. But for SHLD... the Jan 2019 $3 put is currently $1.55, with SHLD at $3.62. If (by some miracle) Eddie paid a $3 special dividend, it would erase those puts.
Any example like that? chance of shld paying $3 is 0.0000000000000000000000000000000000000000000000000000000000000000 bette come up with something better