To my eyes, the leaves of your plant appear a bit narrow for
Corn Plant (Dracaena fragrans). I think your plant might be
Spineless Yucca (Yucca gigantea). Other differences to note are that Dracaena fragrans leaves are soft and pliable with a smooth edge, whereas Yucca leaves have a stiffer texture, as well as very tiny teeth along their edges. Many Yucca species have extremely sharp, spear-like, dangerous leaf tips but Yucca gigantea does not.
I'm not sure what may be causing the stems of your plant to flop over but it doesn't seem normal to me. It may possibly be due to lack of sufficient light, a soil moisture issue, or combination of both.
