This letter introduces a collaborative gripper designed for safe interactions during wearing operations. In a robotic system helping people to get dressed, two main goals have to be achieved: i) the gripper that potentially comes in contact with the person has to be intrinsically safe and ii) the gripper should be able to keep the cloth during dressing, e.g. while passing the arm inside the sleeve of a jacket. This letter proposes the DressGripper, a gripper that addresses these issues by combining a compliant and safe structure with an additional magnetic actuation at the fingertips. This combination enables a soft interaction with the robot while guaranteeing the necessary grasping tightness. Experiments with the proposed prototype demonstrate its applicability in robotic dressing assistance scenarios.