The way that light refracts in in this forest changes properties of whatever passes through it. People escaping to the transient forest will be naked in all ways, and staying too long could cause the forest's transmutive power to eventually mutate their bodies. In a way, you could be claimed by the forest - but transmutation wizards enjoy this environment for how much more fluidly they can work with something here.
One example is Dragonborn who's scales are known to turn crystalline, making them an anomaly. If the Dragonborn escapes quickly enough, this mutation will not have gone deep enough underneath the skin so it won't have affected the organs. Stay too long, however, and that Dragonborn will perish should it leave the Transient Forest.. When one such Dragonborn left, they were exhaling dust, coughing an hacking up crystal as their organs turned to crystal and ground against eachother.
Daytime. When natural light of the sun pass through its leaves, swords an metals can transmute entirely to something else - that which monsters don't feel or fear. Wood, water, it changes manufactured objects back to origins in daylight. This forest wears away natural things or any magic item with high permanency, something of rare or higher - but it is relatively safe for creatures to pass through during these hours.
Nighttime. At night the leaves give off their own light so anything that isn't manufactured might rot or rust or turn into some other (opposite) material. It is advised creatures wear metals an things refracting light to keep safe. During the night, creatures' skin are known to turn scaley, rocky, or wooden.