Eigen John T was telling me about a student of his that collapses her left arm when playing on the A string. This is fairly common, and universally destructive, as it causes tension, injury, and unreliable intonation. Try this exercise at the next lesson, and see if it helps:
1) Put all 4 fingers on the C string. This tends to be the string where most students have the best looking technique. The two things to look for are a flat wrist, so the top of the hand is in line with the elbow, and a thumb that is resting lightly between 1 and 2 or 2 and 3.
2) Keeping the hand/elbow ratio, take that left hand shape and, by lowering the elbow, drag it across to the A string. The idea to a lot of the corrections I suggest is getting the larger muscle groups to do the hard work, so that your fingers are left with small, dextrous, light work. Fyi: If you want to be precise: the arc that the elbow should travel in transit from C to A is not going to be more than 20 degrees.
3) If your student ever needs a complete reset of left hand concept, I like to start by simply grabbing onto the neck as if I am going to pick the cello up, and from there, you should see a flat wrist, a lot of the top of the hand, and nothing weird like a raised shoulder or torqued hand. From here, slowly move the arm down and back, and open the fingers onto the fingerboard. The good old fashioned C scale is what I would prescribe here to work on keeping everything solid and sustainable. Have her practice in the mirror and ask her to be pickier than even you are when it comes to being aware of the collapsing habit.
4) Eigen jokingly talked about taping a metal rod to the inside of the arm to keep it straight. As an exercise, I would forgo the rod and instead rubber band 2 popsicle sticks there instead! These sort of remedies are easy, very physical, and sometimes work when finesse and nuanced description do not. If you try this, I would also suggest cupping the student’s elbow in your hand, and moving it as she traverses the strings. Moving onto the A should feel like down and back, if the goal is to preserve a flat wrist.
So leave the caving to the spelunkers, and let us know if any of this helps. Happy (early) summer!