It depends from poison to poison! An organic poison will lose its toxicity all together in few years but there are a few inorganic poisons that become more toxic but are slow.
So let's deal with organic poisons first! Many organic poisons like herbicides and insecticides break down over time, this means that after they expire they will have to be used in a larger amount to be lethal. But after a few years, these poisons might become totally harmless and can not be used as a poison anymore. Now, surely everyone will be wondering that after something expires it turns bad so why is it not the case with poison. Well, it is the same case if you see really really carefully because when products expire they lose the ability to fulfill the need they were supposed to, so the need for poison is to kill someone, and when it expires it loses the ability to do that.
Now, coming inorganic poisons like Arsenic and mercury compounds do not break down, these poisons have an expiry date because they chemically change when exposed to moisture. This not just makes it harder to use, but this also means that it will work rather slowly now that means a poison that could kill an animal in a few hours might now take a few days to do so. Poisons that have proteins in them decompose over time, changing themselves into another completely harmless compound.
Also, fun fact the chemically altered form of Arsenic is more deadly because it requires a smaller dose to be lethal, but the catch is that it is a slow poison and not as fast as the unaltered form of Arsenic.
Ooooh... that sounds cool 😎