Resigning is a way of ending the game unknown to weak players – Dr. Eliot Hearst
At lower levels it's not uncommon to see a player blunder away a piece and their opponent soon returns the favor. Or, a player to walk into a mate that his opponent doesn't see. At higher levels it's unlikely, but sometimes a miracle does happen.
Years ago I won a Knight at move 10 against an IM. When he realized he was going to lose a piece and stuck out his hand, which was shaking like a leaf, and for a second I thought he was reaching out to shake hands and tell me he resigned. He wasn't doing either...he was making a move and played on. He started throwing everything he had at me. I started seeing ghosts, threats that weren't real, and eventually counter-blundered and lost the piece back. That put us back on even terms and, being an IM, he eventually outplayed me. We were both so frustrated and angry with our play that neither of us felt like doing a post mortem. On the way out of the room I saw him wad up the scoresheet and toss it in the waste basket.
It sometimes happens that even in master play a player will resign when they shouldn't have. It's rare, but it does happen as we see in the following game. White resigned because he saw that he was in danger of getting mated and didn't see anyway out. There was a refutation of his opponent's dangerous attack; he just didn't see it.
Never resign as long as there is a chance the opponent can go wrong. And, before you do, look for a swindle! Usually, that means a forcing move of some kind: a check or a capture, or a threat to do so.
A word on forcing variations. During a game you have to make two kinds of calculations. The tactical kind where there are forced moves, captures, checks and mate threats. Calculating these positions are the easiest and sometimes you can go fairly deep. The other kind of calculating happens in positions where there aren't any forcing moves, which is most of the time. In those positions, because nothing is forced, it's more difficult to know exactly what your opponent will do. In that case, often you can only calculate two or three moves ahead, and the important thing is the correct evaluation of the position. That is why studying positional chess is just as important as working on tactics.
During a game you will have to perform both kinds of calculation, forced and general. But, as C.J.S. Purdy always reminded his readers, the forced kind should always be the first thing you look for because tactical opportunities can pop up anytime, even in inferior positions.
In the following game, white thought mate was unavoidable and resigned. But, had he looked for a forcing move instead of a defensive one, he could have saved himself.
In analyzing the final position GM Andy Soltis mistakenly claimed that white could have won, but Soltis overlooked the best play by both sides as white could have obtained a draw.
Soltis gave the position after black's 34th move in his book The Inner Game of Chess along with some very poor analysis. I enjoyed the book a lot, but I’m not sure I learned anything. As I pointed out in a post a few years ago, like all books published before engines made us all armchair Grandmasters, a lot of analysis contains overlooked tactical resources. However, just because an engine finds a resource the annotator may have missed, that doesn’t take away from the game or its instructional value.
In the final position when Soltis annotated it he either ignored black's best defense to prove a point or just didn't consider it. I noticed that he wrote the chapter this position was in before he wrote the chapters on Monkey Wrenches and Oversights!