Looking at my chairs, it's hard to understand how her fingers got caught (not saying it didn't happen, though). At any rate, velcro probably won't work since the only place to attach it is at the front of the storage compartment and under the seat. That requires sticking it to fabric under the seat, which won't hold for long.
It might be possible to install two slide bolts under the rear of the seat and drill holes partially into the sides of the chair frame for the bolts to catch in. Stay away from the joints in the wood, though. The photo is for example, although it's not quite what I have in mind (can't locate a picture of it). You can probably find cheaper and sturdier ones at a hardware store.
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