BBQ meat that is fully cooked can last in the refrigerator for 2 to 3 days without going bad.
After 3 days in the refrigerator then the BBQ meat might not be good any longer and should probably be thrown out.
If you want to keep the BBQ meat longer than 3 days you can put it in a freezer safe container and place it in the freezer and then the BBQ meat should last up to 6 months when frozen.
The freezer will keep the BBQ meat colder to prevent bacteria from growing on the meat.