It sounds like Ayane has a very weak immune system. It is kind of cruel to put it this way, but maybe Micchan is her backup plan.
People with weak or suppressed immune systems won't necessarily die immediately or even before an old age. It depends entirely on luck and on exposure to sicknesses. Ayane could catch a flu that develops into pneumonia and die suddenly out of nowhere. In fact, that's basically how most people with weak immune systems die. Sudden illness -> gets worse -> death.
Perhaps with the risk of death at any time being a real thing, she sets up Micchan to take over for her if she dies. It is also possible she'd push Sana towards Micchan herself just because that risk of death can be scary if you really care about not hurting somebody.
Honestly, I don't believe that is true in this case. Sana is so obsessed with Ayane that her death and her breaking up will probably hurt nearly as bad. However, it is totally possible that Ayane doesn't realize this.