If a roommate leaves without finding a sublet and their name is on the lease and they did not discuss it with the landlord, legally they have to continue to pay. On the other hand, if their name is not on the lease and they decide to move out, there is no proof that they ever lived there, and they will not be legally held responsible to pay. Also, keep in mind that unless you all have individual leases you are all jointly liable for the lease so you can be charged for their portion of rent if they refuse to pay. You should attempt to find someone else to move in as soon as possible.
For more information about roommates, check out Step 2 of our Rental Timeline.