Accordion Doors Keeping Them Locked?

We put our daughter in a toddler bed, and because she is a climber, we put her dresser in the closet and went to buy a zip lock so she couldn't get in. However, we were unable to find one that would reach both of the door handles as they are accordion doors and the handles are far apart. So thinking that I was a genius, I used a shoestring with a slip knot knowing that if she opened the doors I would be able to hear her and stop her. Totally backfired, she was able to pull the door far enough apart so she could squeeze through and then got stuck in between them. After a heart wrenching 30 seconds I was able to free her. My question is, does anyone know a way to lock these doors? All of the rooms in our house has them so I can't just move her. I know we could try to anchor it, but we rent and I really want to avoid putting holes in the walls if I can.