Are there any situations where a game's clock might be stopped that is not full or half time? Or is there nothing that could stop the clock that would not cancel/postpone the game outright?
To take a pertinent example, the referee and tournament officials will be sensible when a serious injury happens to player. If the match needs to be stopped for an extended period of time, for example to allow an ambulance to attend to a player, nobody is going to say "keep the clock running and we'll play 3 hours of additional time".
There is no outside clock under FIFA (IFAB) rules. The referee decides how much time will be added at half-time or at the end of regulation time. If the officiating crew has communication equipment, the referee will advice the 4th official of the added time. The 4th then holds up the board indicating the minutes added.
However, NCAA soccer have time clocks. When time runs out the timekeeper sounds the horn to end the half or the game. If the ball was kicked towards the goal (keeper not able to get the ball, but the horn sounds before ball crosses the goal-line – no goal is awarded.