While an old jacket may keep you afloat initially, if the flotation material is degraded, it will slowly absorb water and after a while you'll find you're floating lower in the water than when you first went in.
Likewise, after having "floated-around" for a while, if the flotation material has "taken-on" water .. you'll notice the jacket is noticeably heavy, "squishy" and slow to dry off!