You need to be very careful with the string/lace/collar you use to attach the bell, it should be strong enough to resist casual attempts to remove it, but not strong enough to not break when some substantial force is exerted on it (weight of the animal).

Single point anecdata, but I once found a cat with a collar that remained stuck in a fence, the cat - attempting to get it off - managed to insert a leg inside the collar and that - with more attempts to get free - made a really deep cut under the armpit, the poor cat was half choked and it took weeks for the wound to heal. .