On Tishah b’Av, we rearrange the furniture of the synagogue. The curtain hanging before the ark is removed, and people sit on low chairs and benches. Some sit on the floor. These are marks of mourning. As in the shivah period after a personal bereavement, sitting low down is an expression gesture of abasement and grief.
The Talmud discerns a reference to this practice in the Book of Job. When Job’s friends come to comfort him on his losses, the text says literally that they sat with him “towards the ground” (la'aretz) for seven days, implying that they were close to the ground (Job 2:13).
The folk belief that mourners sit low down to be closer to the dead in the earth does not have a basis in Jewish tradition that I am aware of.
The Talmud (Ta'anit 30b) teaches that on that Tishah b’Av people used to turn over all beds and couches so as not to sit on them, signifying that on this day we are all mourners.