[thepossum]

Just asking for a friend

Said friend could possibly have gotten away with a King or a void. Maybe even a singleton

But no

It wasn't to be and said friend's partner is a bit disappointed

[hrothgar]

Sort of (but typically not)

There are all sorts of different ways in which the notion of a "control" gets used in bridge.

If people are playing a natural style, controls often come into play during cue bidding sequences.
And, in a perfect world, the partnership has agreements about what does / does not constitute a control.

One such agreement might be whether the initial cue bids show first round controls or first / second round controls.
Another might be whether a cue bid promises an honor or might instead be bid with shortage.
Sometimes, you'll have agreements that you can't cue bid shortage in a suit where partner has shown length.

In these examples, I'd be quite surprised to see someone cue bidding a small doubleton unless this was done as a psych.

However, there are other styles of bidding and some of these rely on Control Asking Bids.
Many CAB systems have ways to show a small doubleton.

[pescetom]

I would just add that if a partnership agrees to show indifferentiated first/second level controls in the Italian style, then it will occasionally be possible to show third level control (Q or small doubleton) having already affirmed or denied the first two levels of control in that suit.