Yes when you lose weight your shoe size will usually reduce in size as well.
Especially if you're really overweight to begin with you'll usually have more fat around your feet and need bigger shoes to allow your feet to fit into them properly.
When you lose weight the fat around your feet will also or should also shrink along with any other fat around your body.
So you may need to get a smaller shoe size when you lose a significant amount of weight.
If you're just losing 50 lbs to 100 lbs of weight and are not really overweight anyway then you may not need to buy a smaller size shoe.
When I lost 40 lbs of weight my shoe size stayed the same but if I were really overweight then I would have likely lost fat around my feet as well and need new shoes.