When a school makes a funding commitment, it is generally true that the commitment is contingent upon a student making satisfactory progress to the degree, as judged by the department.
What happens when a student can't finish in the stated period depends upon a combination of factors:
- Where the funding to continue supporting the student will come from
- If the student is, in fact, making adequate progress and will finish in a reasonable period of time
- What the regulations of the department or university are with respect to enrollment (that is, is there a limit to how long a student can be enrolled)
So long as a student is making satisfactory progress, and a source (such as PI funding or teaching assistantships) can be found to pay the student, departments are usually not inclined to dismiss a student based on failure to meet an arbitrary timeline. Usually, the student, supervisor, thesis committee, and department will agree on some sort of timeline to finish the degree program as quickly as possible.