The ring confers absolutely no benefits to a dead character who is given the ring after death. The ring must be worn at the time the character “dies”.
A character who hits 0 or negative HP at the time the ring is being worn will not require 0 HP bedrest when brought back to positive HP. The 1d6 turn coma period still applies. A character who is given the ring after hitting 0 HP or lower will recover HP at the normal rate, but will still be subject to the standard week of 0 HP bedrest.