As described in the beginning of this question, collenchyma cells are found in young stems and petioles (leaves) and function to provide flexible support to the plant. This is because chollenchyma cells lack secondary cell walls and do not produce lignin to harden them—this protein is characteristic of sclerenchyma cells, which are also used to provide support/strength to the plant.
Due to their lack of rigidity, collenchyma cells a also capable of elongating with the stems and leaves they support, allowing them to remain alive at maturity. Sclerenchymal cells lack this ability.