If oxygen is not present, there is no electron acceptor to accept the electrons at the end of the electron transport chain. If this occurs, then NADH accumulates. Once all the NAD+ has been converted to NADH, the Krebs cycle and glycolysis both stop (both need NAD+ to accept electrons). Once this happens, no new ATP is produced, and the cell soon dies.
And then there was anaerobic respiration.
Anaerobic respiration is a method cells use to escape this fate. The pathways in plants and animals, alcoholic and lactate fermentation, respectively, are slightly different, but the objective of both processes is to replenish NAD+ so that glycolysis can proceed once again (producing 2 net ATP). Anaerobic respiration occurs in the cytoplasm alongside glycolysis.