The general question is unanswerable for all cases. It is also too unspecific regarding the timeframe. The policies and purposes for all such camps changed over time. A concentration camp was operated differently in 1933 compared to 1943 or 1945 and the so called extermination camps a different again.
Except that one thing is sure: the Germans in the SS tried to kill every Jew, really hard. That was the plan, officially, after the Wannsee-conference. If a person was to be shot and the pistol was jammed then the person would be shot by another one, beaten to death, etc. There was certainly no general contingency plan for what to do when the first attempt to kill anyone didn't work as planned. Only the end result mattered in the 'final solution'.
But for Gena Turgel (born Goldfinger) the case seems to be known:
At one stage she survived the gas chambers, when the mechanism broke and she later said this narrow escape convinced her she had a duty to bear witness to the Holocaust by speaking to schoolchildren about it.
Telegraph: "'Bride of Belsen' who survived four death camps dies aged 95" (9 JUNE 2018 • 3:06PM)
That means that a whole "batch" of people walked in and survived. Meaning that only case 2 from the question is remotely applicable here:
The guards did notice it, but did not try to gas her again.
Or as Danila Smirnov commented:
Another survivor's account mentions guards running out of gas and returning victims back to camp. Since both incidents happened in the same camp, the reason probably was similar - the gas chamber was not in working condition for some reason.
And after the gassing attempt the time was running up for the death camp:
In January 1945 Gena and her mother were sent on a death march from Auschwitz, leaving behind Hela, Gena’s sister. They never saw her again. After several days they came to Włocławek (Leslau in German) where they were forced onto trucks. They travelled under terrible conditions for the next three to four weeks, eventually arriving in Buchenwald concentration camp. From there they were sent on cattle trucks to Bergen-Belsen, where they arrived in February 1945.
het.org.uk: Gena Turgel MBE
This story is one of a certain degree of luck and timing:
On 26 January 1945, the last crematorium V at Birkenau was demolished with explosives just one day ahead of the Soviet attack.
WP: Auschwitz concentration camp
That brings us back to the opening paragraph: after the failed gassing they tried to kill Goldfinger on a death march.