The payoff chart ends cleanly at expiration. Real positions do not — they settle through an allocation process that has its own rules and its own surprises.
A short option that finishes in the money is automatically exercised, and the clearing house assigns that exercise to a short holder. The result is an obligation, not a decision: you buy the shares on a short put, or deliver them on a short call, at the strike.
This is the mechanism the whole structure was priced around. The premium you collected was payment for standing ready to do exactly that.
American-style equity options can be exercised at any time before expiration. It is rare, and it is not random. It happens when holding the option is worse than holding the shares or cash it represents, which means deep in the money with almost no extrinsic value left to lose.
The classic case is a short call with a dividend approaching: exercising the call captures the dividend at the cost of the remaining extrinsic value, so it becomes worth doing. Put assignment tends to appear on deep in-the-money positions where the cash tied up in the strike has value of its own.
Pin risk is what happens when the stock finishes within cents of a short strike. Two things go wrong at once. Whether the option is exercised may be decided by the closing auction rather than by the screen you were watching, and any long wing you hold may resolve the other way.
The result is a position that was fully hedged at the bell and is not fully hedged afterwards: short shares you did not plan to own, or a bare option leg over a weekend, with no chance to close it until Monday. It is a small probability event with a large consequence, which is why it belongs to position sizing rather than to prediction.
The practical question is not whether assignment will happen but whether the position still does what you intended if it does. A short put written on a stock you would accept owning is a planned assignment; the same put written for premium alone is an unplanned purchase at a price you did not choose.
Near expiration, the operative decision is usually whether to close a position that has drifted to the strike. Holding it to the last day is choosing to accept whatever the auction allocates, which is a legitimate choice as long as it is a chosen one.