Stellar fusion and supernovae are governed by quantum particle interactions (on massive scales). In general there are many possible ways for particles to interact, decay, etc. at various probabilities. To understand the physics of a system correctly you must take account of all possibilities (up to an error tolerance in actual practice).
One often sees phrases of the form "situation X favors reaction Y". This means the conditions (X) make the the probability of Y greater than any other possible reaction, but it doesn't equate to Y having probability 1. Some may prefer to use this phrasing for when Y's probability is, in some sense, much larger than any other event.
The proton-proton chain that governs the main sequence stage of a star is a prime example of why you cannot discount the reactions which aren't favored. If you did, you would conclude that our own sun is incapable of fusion. The 'favored' reaction for two interacting protons in a star like our sun is to simply bounce off of each other thanks to Coulomb repulsion. The protons simply don't have enough energy to overcome this repulsion in order to undergo fusion. Technically this statement is also not probability 1, but rather very close to it. But an improbable quantum tunneling event is possible to bypass this potential barrier, allowing the interacting protons to fuse when they collide just right and the dice favor them. But a diproton is unstable. The heavily favored reaction in this state is for the diproton to immediately decay into two protons. But there is a small chance that one of the protons will undergo a beta decay into a neutron, instead, at which point you have a stable helium nucleus. That these things are so unlikely is a major factor in why our sun needs billions of years to exhaust enough of its hydrogen (aka protons) in order to initiate helium fusion and exit the main stage. Even very large stars still need millions of years because of this.
So while the proton-proton reaction is rather unlikely, stars are simply so immense that it is not only a virtual certainty that some proton-proton reaction will yield helium, but in fact that it is a virtual certainty that the reactions will occur in large numbers and continuously until the available reactants dwindle.
At the other extreme, we have supernovae. There are quite a lot of varieties of supernovae, but the commonly understood types--the outer layers collapse and then violently rebound off the core--feature a sudden loss of radiation pressure due to certain endothermic reactions becoming favorable. Iron production from fusion is the culprit here: it takes more energy to fuse it than is released. The final split second of this sort of star's life is when conditions favor the production of iron via fusion. Ridiculously favors it, as I really do mean it is the final split second. There is an inconceivably tiny chance that this iron production would fail to occur for some chosen period of time, and if it happens to stall long enough then the star would likely undergo some other event. See also David's answer for another wildly improbable, but technically possible, example of random chance altering a star's death.
