It seems that all of the characters of this excellent play are engaged in some form of escape, one way or another. However, undoubtedly, the character who is most detached from reality and most wishes to escape it completely is Laura. She is shown to be unable to have normal interactions with other humans without physically being sick, as her mother discovers when she discovers the truth about her typing classes. The focus of all of her energy is an inanimate collection of glass animals, which of course do not have any reality. Note how this is emphasised by her special affection for her favourite, the unicorn, which is a mythological creature that has no basis in reality whatsoever. She has constructed a world for herself in which she can exist the real world.
However, ironically, what should have resulted in her return to the real world, the breaking of the unicorn's horn, only seems to remove her further into her realms of fantasy. Note what Laura says when she realises that the unicorn's horn has been broken off:
Now it is just like all the other horses.
However, if we take the unicorn to symbolically refer to Laura, what could have made her just the same as other humans, her relation with Jim, is taken away from her, and she is left to retreat into her escape world once more, but only this time she seems to retreat into it even further and more deeply.