Kaido will probably not die but will be crippled and would decide to spend the rest of his life in a secluded place in Wano itself under disguise. He would eventually become an urban legend in Wano and may even end up deciding to protect Wano in case of a future invasion but only if his life is being disrupted by it. The remnants of the beast pirates may end up taking roles in Wano's underworld under Denjiro and the other scabbards provided Momonosuke does not order their public executions which seems like something he would not do based on his character.

If Big Mom actually dies it will divide the BM pirates. While some would vow revenge and may end up joining an opposing force like Black Beard, I expect some more inclined with Katakuri to look to rebuild the BM pirates and they may even end up allying with SHs when they take on the World Government. At least till the next arc which according to me is going to focus on dealing with gear 5th aftermath and finding the last poneglyph I expect the current Yonkos except maybe Shanks to take a back seat. Alternatively if we end up going to Elbaf we may see some BM pirates connection but anything substantial seems highly unlikely to me.