Here's how this problem is motivated in my head… The more obvious way to get an AI system to shut down is to have a shutdown action. Then utility-maximization occurs in an inner loop that is overridden by instructions to shutdown or change the value function. But then you need the utility-maximizer to be corrigible somehow, perhaps using a shutdown utility function, making this a purported subproblem of corrigibility.
As for obvious proposed solutions, if you had defined a shutdown action [e.g. run this routine that switches the power off], then you could have the objective "The chance of this action being performed is greater than 99.999%" as your utility function. Though an incorrigible AI might be able to copy itself to get around this…
One also wonders if this could be adapted into a reductio ad absurdum of the idea of making aligned AI by specifying a sovereign's utility function.