Actually this is kind of extensive list and not every project would look the same. If you think about agile projects, well, forget steering committee, etc.
Anyway, the PM job definition I once heard I like a lot is: "PM responsibility is to get to job done." Sure PM doesn't make it all with their own hands but they try to coordinate everyone's effort so the final result is satisfactory when compared with success criteria (whatever they might be).
From the perspective of such definition PM can basically use one of a couple of approaches to inactive sponsor, or a mix of them.
Fight with it. When PM needs something from the sponsor they ask, beg, threaten, bribe, convince or whatever it takes to get it. It's like overcoming sponsor's inactivity. When they don't act whatsoever by themselves let PM force them to act. This approach, if applied successfully may change inactive sponsor into an active one. But then remember: be careful what you ask for, because you might actually get it and sponsor's activity might not be exactly kind of behavior PM would expect.
Accept it. When PM potentially needs something from the sponsor they look for any other path which leads to the same result: getting information from someone else, finding other people with enough authority to make the call, making decision by themselves and asking for forgiveness instead of permission etc. Pretty often no one would even notice. Having said that it can be somewhat risky - if the end of the project is marked with a failure and blame game starts, guess who will be the first target.
And then of course there are all kind of mixtures of those, like using the latter in most cases and retreating to former when there's no other choice or potential consequences of choosing poorly are very high.