Mishka Dilemma

We just found out that the owner's of the house we rent want to put it on the market so we have to move. As much as we want to take Mishka with us we have decided it would be cruel to remove her from the only area she knows. Given another year we probably could have got close to her. The only thing we can do is talk to the neighbors behind us and see if they can take on the responsibility of feeding her. Trapping her and trying to make her an indoor cat would not be kind for a cat who has lived outside like this. Abbey is de-clawed (not by us) and couldn't defend herself if they got into a fight.

I do not want to leave her.