Sometimes Google images can provide a picture which approximates what you are seeing. See for example this Alocasia with snake-like stems which appear to be just elongated upright stems that have flopped over due to gravity. In this case the clue to identity lies in the top growth; you might have to look around for a sample which clearly indicates through flower or fruit what species it is.
For propagation we normally look for tubers or suckers. Suckers are produced at ground level so either way if the roots are covered then it will be necessary to uncover to get at this ready rooted material. However you could consider a technique called "air layering". A search on pictures of air layering Alocasia may produce examples of successful attempts to get this to work, but it will likely take longer than searching for some suckers.
Update: in the above linked photo the plant is/was at a botanical garden in Tenerife, Canary Islands (Jardín de Aclimatación de la Orotava). If rooting is likely along the stem then the gardeners at that location should have a good idea whether their specimen has done so since there is a good length of stem on the ground in a warm location. You might do well to contact your local University Botany department who will likely have a direct professional contact with Tenerife and could make an enquiry by email. That way you would get direct to the guy with a trowel who could look for roots. Also consider a contact with Hawaii where the plant is an important crop.
Caution: Taro family needs to be treated with respect due to irritant sap and cell structure.