There are countries, like the US and UK, that occasionally provide temporary homes for people from other countries who have been displaced by natural disasters, as noted by Ann Danylkiw on SolveClimate. But what happens when the natural disasters are long-term problems that can't be resolved simply by clearing up the debris and rebuilding? This is the poser presented in an analysis from the International Organization for Migration. There have always been people displaced by short-term climate events such as drought, but with climate change the effects are long-term.
There is no internationally-agreed category for people who undertake climate-induced migration, making it difficult to this type of migrant to apply for refugee status. Complicating matters further, some migration is likely to take place as an indirect result of climate change; for example in response to conflict arising over scarce resources, or because of poor governance that renders states or regions unable to manage economic and social stresses arising from climate change.
This is just one more reason why adaptation strategies are absolutely crucial in the UNFCC negotiations. Communities need greater flexibility and access to resources, and that's not going to change significantly unless local governments are willing and able to adapt their own planning processes and international agreements provide the necessary support.