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Jet fighters are made to cruise at a high subsonic speed, even at a supersonic speed (supercruise?). It means that they can be flown comfortably at relatively high speeds.

Jet fighters are often used to intercept aircraft, whatever the reason (assistance, escort from national to international airspace, check an unresponsive aircraft,...).

General aviation aircraft can cruise at a slow speed compared to jet fighter. Moreover, if needing assistance, it may fly even slower. I imagine it is possible that a GA aircraft needing assistance cannot fly at a speed above the stall speed of a jet fighter. I know that some countries dispatch choppers to intercept slow aircraft to handle such situation.

I imagine the military doesn't fly their jets at stall speeds when close to another aircraft (a margin is needed).

Is there a speed below which a jet fighter cannot intercept another aircraft? Otherwise, how do they do it? (I imagine you can orbit above another aircraft but it is less convenient to guide it safely to an airport)

There is nothing stopping a faster jet from flying a zigzag pattern behind an intercept target if the goal is to remain in close contact with it, but a large difference in airspeeds would indeed hamper some tasks like observing the cabin for signs of life or unlawful interference. So the answer is yes, a jet fighter cannot perform all the tasks involved in a typical interception of an unresponsive aircraft if the speed delta is too high.

For reference, the take off speeds of 4.5 generation fighters like the F-16 are in the 130kt (240km/h) region, while the take of speed of something like a C172 is around 60kt (111km/h). The exact weapon and fuel load of the fighter will of course have an impact, but fighters scrambled for an intercept are typically light and with an almost clean configuration. I have deliberately used takeoff speeds instead of landing speeds to factor in a margin of safety in regards to control authority; both speeds are among the lowest an aircraft can sustain, but during close approaches to a potentially hostile aircraft, some maneuverability is required.

Still, 100+ km/h is a substantial speed gap, and has led to issues in the past:

The Po-2 is also the only biplane credited with a documented jet-kill, as one Lockheed F-94 Starfire was lost while slowing down to 161 km/h (100 mph) – below its stall speed – during an intercept in order to engage the low flying Po-2.

There is almost no assistance a military jet could provide to a GA aircraft that would require the two to be in close formation at the same airspeed.

The nearest situation necessitating formation flight would be to provide visual verification whether landing gear were fully extended. While close up inspection of an over-center lock is possible to confirm, a general up, down, or stuck halfway assessment is possible from quite a bit further.

Even if it were ideal or possible, unbriefed formation flight between dissimilar aircraft with a GA pilot of unknown proficiency presents its own set of risks.

Communication relay to ATC, assigning headings to a hole in the clouds, etc. are legit forms of assistance that could be provided from an interceptor orbiting higher overhead at a different airspeed.

Military fighter jets are actually not all that fast, when they aren't supersonic. Their cruise speeds are below the cruise speed of airliners. Supersonic flight is mostly meant for interception, while combat speeds are low-subsonic. The best-range cruise speed for most fighters in the range of 300 knots, due to high drag, and the speed for the tightest turns goes as slow as 200 knots.

Below their maneuvering speeds, there is considerable margin to an actual stall. It depends on weight and altitude, so there is no one answer, but it goes down to 100 knots and below.

The most popular GA aircraft, the Cessna 172, has an official cruise speed of 122 knots. This is within the operating limits of most jet fighters, except when overloaded or at altitude above that of GA aircraft. So there is a sufficient amount of overlap between GA and jet speeds, if both want to stay alongside.

However, a GA aircraft can operate much slower, and jet fighters generally won't be able to maintain a steady position close to their stall speeds. While their TWR can be close to 1, the typical fighter aircraft is simply not controllable at a 45-degree angle of attack. Make no mistake, a fighter won't lose a GA plane, but it won't be able to maintain a steady position next to it.

Fighters with thrust vectoring, which are still rare, could sustain mostly side-by-side contact with a GA aircraft. The Pugachev's Cobra maneuver can slow a supermaneuverable plane to near-zero airspeed, although it will have to get back to its stall speed after.

That said, a helicopter is still more practical for assisting a GA airplane, not least because it's much more likely to be able to land near the plane's crash site to help pull the occupants out.

This would be a good one for the V-22 Osprey, with a flight envelop of 0 - 350 mph.
Another possibility would be the F-35B VTOL version.

The jet intercept would be step 1 to communicate/identify. Many helicopters could also follow up if more assistance was needed.

Interesting to note that the Po-2 biplane would be cruising around 60 mph, in the GA range.

"Outslowing" an intercept is no longer a survivable option. Accomplishing the task is a matter of using the right tool for the job.