A.M.
Two of my children both have friends who have "accidents" at night. They are both school age children who have been over for sleep overs at our house. My son's friend had brought overnight pants and his mother explained that he had accidents sometimes. My daughter's friend also brought overnight pullups and her parents said the same thing. I noticed with both of them that they were extremely hard sleepers. If I had to move them into a bed at night, or cover them up, neither one moved. Neither's breathing patterns changed or anything. Maybe your 3 year old has become a heavy sleeper?
The parents' advised us to not give them drinks after 7-8pm and make sure they use the restroom before bed. They still had accidents sometimes, but it helps.