Hypermobility in simple terms is too much mobility through some joints. This is very common and different people are affected in different ways.
Some people have abnormal collagen (usually inherited) which leads to joints such as fingers, elbows and knees having too much extension. Other people have shallow joints (also usually inherited) which lead to joints such as the shoulders and hips having too much rotation and abduction. Females are more commonly affected than males, often with elbow extension. Joint hypermobility can also be developed, for example gymnasts and dancers typically have lower back extension, hip abduction and rotation.
Normally clients have no pain associated with hypermobility. However, joints with excessive extension will be less stable when weight bearing. A table leg is stable but if you bent it slightly in any direction it would be less stable and you wouldn’t trust it to hold your table up. A hypermobile elbow in 4-point kneeling is likely to be bent (beyond where is ideal). For the client, this feels normal. This is effectively their ‘straight arm’ position - they have gone to their end range. Anatomically, through no fault of their own, their end range is beyond what would be considered to be ideal (straight), giving them a less stable joint structure in this position. For them to hold the arm in an actual straight position requires constant effort, similar to having to bend your knees slightly. It is far easier to reach your end point and push your weight through your skeleton than it is to consciously be aware of where ‘straight’ is and then to stabilise and contract the muscles around the joint to keep it in that ideal position. So structurally hyper-mobile clients are at a stability disadvantage in their affected joints. However, this doesn’t make much difference to daily living or the performance of Pilates exercises.
Hypermobile clients will usually be aware of their joint mobility and may ask you for advice. In my experience as a hypermobile person and Pilates instructor, you can’t fix it by making shallow joints deeper, or altering joint collagen. However, you can make the surrounding tissue stronger and in turn learn where ‘straight’ is to stabilise the joint. To begin with your clients may need reminders as it is a huge effort to alter how you stand (if knees are affected) or how you perform in certain positions. As long as they are ‘set up’ correctly for each exercise and encouraged into ideal positioning throughout, then you are doing the best you can as an instructor. The rest will need to come from their increased body awareness and willingness to learn.