I think they're both alive.
Big Mom will show up shriveled up. Her defeat and the use of years of her lifespan on her fight with Kidd and Law will take it's toll. She'll still have power and authority, but it will be time for the next gen leader of the Charlotte family. Probably Katakuri.
Kaido is alive as well and will show some respect to Luffy because of the Joyboy story with Alber.
When both of them, the Yonkou, show up eventually supporting Luffy on the final conflict against world government, even if kinda angry about it, we'll know Luffy is King.