adobe photoshop - Shrinking or expanding object with retaining it's original shape

First of all, I am sorry, but I don't even know how to address this question properly. It's best illustrated by pictures below. So question is: Is there some way, in any graphic program (both vector, or raster), how to resize an object, so it keeps it's original position and retain it's original shape, meanwhile it can be fit inside or outside of itself's original? (I know it's hard to understand, but hopefully the picture will tell more)

Below are two images - one on the left was made by selection contraction, however, it doesn't solve the problem, cause some part of the object are lost, when shrinking too much. The one on the right was made by moving path points, which was done by moving all the points accordingly one by one... The goal is to achieve something like image on the right but of course by some automatic process.

Thank you