During a simultaneous blindfold display by Alexander Alkehine against thirty two Nazi Generals during the Second World War, the following position was reached. Only four games were left, Alkehine haveing won most of the others, drawing a few.
When he came to this board and asked for his opponents move, the general offered to resign since he could not see how he could stop White mating on h8. For example, 1 ... g6 2 Qh7+ Kf8 3. Qh8+ Bxh8 4. Rxh8#.
Alkehine offered to swap sides, to which the general readily agreed and play continued.
1... Rh4 2. Nxh4 Qc3
Now the general had to agree that it was white who was losing. For example, 3 Kc1 Qa1+ 4 Kd2 Qxa8.
Alkehine again offered to swap sides. This time the general wanted to consider his decision and Alkehine busied himself with the remaing three other boards. On returning the general again agreed to swap sides.
3. Qh8 Kxh8 4. Ng6 Kg8 5. Rh8#
The moral of the story is "Never Say Die".
For a further example see There is always hope.
Source: Alexander Kotovs biography of Alexander Alkehine