Why is my Chinese elm dying?
Also know, why is my Chinese elm losing leaves?
For Chinese Elm bonsais it's completely normal to lose leaves after keeping healthy leaves for a season. The tree will start losing some old leaves in place of the new buds growing. The leaves dropping off the bonsai is due to a decrease in daylight and temperature as the seasons change.
Accordingly, is my Chinese elm dead?
Chinese elms can handle indoor circumstances pretty good but they thrive best outdoors. You can check if it's still alive by scratching the bark a bit. If the cambium layer is still green the tree isn't dead (yet). If it's brown, well you know it's dead then.
Subtropical bonsai trees such as the Chinese Elm require a lot of attention when it comes to water. If your bonsai is too dry, that would be why your leaves are turning yellow. If it feels dry, you need to water the bonsai. Water the top of the soil until you see water leaving the drainage wholes in the pot.