Thanks for all the replies.
Wildfyr,i would like to mention,that i am not expecting to
make the midsole flexible again.
It,probably,will become stiff and won't be proper for running etc.But i don't care,since my intention is only to make the crumble process to stop.
One of the ideas that P suggested was close to what i was thinking and it to inject some kind of solvent with syringe into several parts in the midsole,that will be absorbed and
make the crumbled polyurethane stick together.
Can you have any idea which solvent/material may do that?
BTW,treating the shoes with something prior to storage,as billnotgatez,suggested,could be a better solution,but it is too late for those shoes.