The localPosition is relative to the parents coordinate space. If you scale your parent for example to 0.01 on each axis, the local coordinate space is shrinked by a factor of 100.
That means, assuming that the parent is at position 0,0,0 in worldspace, a childobject at 200,0,0(local space) will be at 2,0,0(world space).
Your question isn’t really clear what actually happens. Do you mean that even when you assign a new position (no matter if local or global) the position doesn’t change? In this case you propably have either:
a scale of 0.0
another script or code fragment that continously resetting the position
or an Animation attached that animates the position to be at a specific position.