Noooo.... Your ESA does not stop. You will get ESA [now renamed "new style ESA"] AND UC as well.
This is correct, because only MEANS TESTED benefits are subject to migration. Your contrib ESA continues unaffected albeit reduced to £281. Even though the DWP are too thick to even know what ESA you are on, you paid stamp, correct??? You were on ESA contrib with an "income related" top up.
I know it is clear as mud, but all is well with your migration..
john..