Good question Katie.
Yes sometimes they have very little prepared and I can help them strategise and define their project. When I do this it becomes its own separate short-term project/contract. I do info architecture and help them work out the scope of what they need. Then I will use that scope to estimate the cost of the remainder of the project.
Design bleeds over into so many areas of business, and many of my clients get surprise extra value when I consult on digital strategy and help them define what they actually need vs. what they think they want. This could even include things like naming, domain names, branding & personality, product strategy and market fit, etc.
These high-level decisions can have more impact on the success of a project than the creative work to follow later. So if you can add value to that discussion that’s a plus for everyone. Don’t shy away from helping people define those early project briefs if you feel you have the expertise to do so.