Zeus swallowed Metis to prevent the prophecy of her future son overthrowing him from being fulfilled, but she was already pregnant, and later her daughter Athena sprang from Zeus' head. What happened to Metis herself when this happened?
There are two possibilities here:
Either, Metis was killed when Zeus swallowed her:
It may seem odd for Metis to have been pregnant with Athena but, never mentioned as her mother. This is because the classic Greeks believed that children were generated solely from the fathers sperm. The women was thought to be nothing more than a vessel for the fetus to grow in. Since Metis was killed well before Athena's birth her role doesn't count.
However, other myths state that she continues to live inside Zeus and that she is the source of Zeus' wisdom. Since she was the goddess of wisdom, prudence and deep thought:
It is said that she is the source for Zeus wisdom and that she still advises Zeus from his belly.
I believe the second is more believable because Zeus is himself titled Mêtieta, "the wise counsellor," in the Homeric poems and the Wikipedia article for Metis also states that (while she was inside Zeus):
She began making a helmet and robe for her fetal daughter. The hammering as she made the helmet caused Zeus great pain.
Which would mean that Metis was not killed and was living inside Zeus.
I know she escaped. There is a Greek tablet (the tablet was marble, and it's in a museum in Crete) that says when she hammered her essence into Athena's things, she hammered the last bit into a rock. When Athena went to earth, she shattered the stone. Metis bursted from it as an owl.