Do feet get smaller when you lose weight?

Could it be true that losing weight also leads to a reduction in the size of one's feet? I've heard some people claim this, but is there any scientific evidence to support the notion that shedding pounds can actually shrink the dimensions of our feet? I'm curious to understand the anatomical and physiological factors that may be at play here, and whether there are any notable differences between men and women in this regard. Could you elaborate on the potential mechanisms behind this phenomenon, if it indeed exists?