I think it depends what you mean by "unscheduled".
These days airlines usually have a very good idea of how much fuel will be needed for a particular flight, given the load of the aircraft, weather, prevailing winds, expected delays, and so on. However, as these factors vary from day to day, it may sometimes happen that the required amount of fuel is more than the plane is able to carry. The limit is usually not the capacity of the fuel tank, but rather the weight of the fully loaded and fueled plane.
If this happens, an extra stop will be planned. Normally this would be known well in advance of takeoff and included as part of the flight plan, and announced to the passengers ahead of time. (The one time this happened to me, about a year ago, they announced it at the gate, and estimated how much it would delay our arrival.) The usual term for this is a "tech stop".
Of course if this happens a lot on a particular route, the airline would probably want to switch the route to a different type of aircraft with a longer range, if they can. But it may be that the airline doesn't have such an aircraft, or they are needed for other routes, or for some other reason it wouldn't be cost-effective. But the occasional tech stop would probably be taken in stride.
The other possibility is that the flight takes off expecting to be able to reach its destination without a stop, but along the way the pilots discover that they will need to land somewhere else due to having used more fuel than expected. Such an unplanned landing is called a "diversion". This should be much more rare, as fuel planning is usually quite accurate and includes a sufficient buffer to account for the unexpected. Diversions happen more often when weather at the destination airport degrades to the point where a safe landing is not possible.