What are the hazards and risks if I keep using a worn rear tyre?
If it’s just the rubber tread which is worn down and thinner: Keep using it. With treadless tires you’ll only suffer from increased susceptibility to punctures. Of course with knobby/treaded tires your grip on soft surfaces will gradually decrease.

If the tire’s structural integrity could be compromised: Don’t use it. It could fail catastrophically at any time. Things like bulges, abrasions of the sidewalls, cuts or large cracks are all bad signs.