The string can be used to carry a deze, mostly by sellers who need to carry several at once. Musicians may use that to hang the deze on a wall out of reach of small children.
It is important to never carry a calabash/gourd deze by the lip, as that is the most fragile part and easily broken. A few people put bamboo (or another material) around the lip of the deze to strengthen it, but that does reduce the resonance somewhat, in my experience. A fiberglass deze can be carried by the lip if it is empty or has little weight inside.