Active agent guidance
In the typical chatbot scenario, there are two parties: user and the chatbot.
Usually the user comes with a goal. Imagine this simply as seeking for the answer to some question from the chatbot (agent).
For the agent, or an equivalent human, to solve the problem, certain information must be obtained from the user.
Preliminary diagnosis agent at a medical facility
Clinics and hospitals would benefit from prediagnosed patients. However, patients most prorably have no idea what their illnesses are. Another common situation is that the patient has a lot of wrongs going on but cannot sort out what's important and what's not so important.
A doctor will usually start with generic symptoms, narrow down options, then go into more detail, narrow down more, and repeat until a decision could be made.
An agent could mimic this cycle of actions. It's nothing structurally complex, just needs a lot of, experience and long term memory (for correspondence between symptoms and illnesses).
Emergency service first response
Nowadays, when people ring the emergency services (e.g. 119 for fire / medical in Japan), they are expected to provide an address first so the best (usually, nearest) ambulances or fire trucks can be dispatched as the caller provides further information.
In reality, a lot of people cannot do this because they tend to panic. [citation request] Trained emergency service operators will of course try to get the address first with verbal guidance. And that could be something for the agent to learn.
Inferring unspoken information
I saw this one floor below us (the HCI lab on 8F), on one of the posters from Language Media lab (not sure if this is their name in English; 言語メディア学/荒木研).
The idea is, while someone is talking, they could be giving information in an unconscious way. Usually it is not some secrecy that the speaker will actively try to hide, but simply information considered undeserved for a dedicated statement.
For example, when someone says, My older sister sent me a box of potatoes from Tokachi, the main point they're trying to make is that they received a box of potatoes. However, it is also known that the speaker has an older sister. Also she's either residing in Tokachi, or been there recently. The latter is less certain for various reasons.
The moral here is that, for an active agent that will ask the user for additional information, sometimes it can try to analyse and work out some of the info on its own. This will make the agent seem more intelligent, probably getting more trust from the users. Or not, go get some literature.