Do teeth tend to change shape or come forward after we become adults?

Yes and yes: Teeth can change shape over time due to grinding habits, which wear away the edge of the enamel. Teeth also tend to move forward as we age due to the action of the tongue pushing on them as we swallow. Loss of vertical dimension posteriorly can also cause the same effect.

In certain cases: People who suffer from bruxism where they grind their teeth either at night or subconsciously during the day, wear away tooth structure from the biting surfaces of their teeth. So in effect, the shape does change, but not necessarily so for every adult. Regarding teeth coming forward- individuals who lose teeth or have periodontal gum disease can have a bite collapse or spreading out of teeth.