When an application is being transitioned to me, I ask as many questions as I can possibly ask.
And I hear it over and over again.
"Don't worry, we'll be here to support you if anything goes wrong."
That's a buzz-phrase.
"We are going to fling this over the fence as fast as possible, and you'll never hear from us again."
So if you approach the situation from that point of view, you won't leave any stone unturned.
Because first production issue and you're the only resource to put out the fire, nobody's going to want to hear that someone promised to help you out, they are nowhere in sight.
It's your irresponsibility to ensure a smooth transition.
That's my point of view.