Will running cause skin sagging to happen faster?

I'm thinking of starting running these days to lose weight.

I'm worried because I've heard people around me say, "If you run a lot, you lose weight in your face and your skin sags more."

I understand that doing cardio helps you lose weight overall, but,

I am curious if skin elasticity really decreases along with it.

I'm confused about what's right because I've heard that it actually improves blood circulation and is good for the skin.

For those of you who run regularly, have you noticed any changes in your skin?

Please also share any maintenance methods or tips you have.