Alice would not be entitled to a visa at the expiry of her student visa as she falls outside of the rules to obtain one (unless she makes a successful application for an extension or for another category).
Instead, she may be entitled to Discretionary Leave to Remain.
Discretionary Leave (DL) must not be granted where an individual qualifies for leave under the Immigration Rules or for Leave outside the Rules (LOTR) for Article 8 reasons. It only applies to those who provide evidence of exceptional compassionate circumstances or there are other compelling reasons to grant leave on a discretionary basis.
One of these "compelling reasons" is covered by the Home Office circular 2 / 2006, which:
...provides guidance on the procedures for dealing with persons who are subject to immigration control and required to give evidence at criminal prosecutions in the UK...
- Persons already in the UK
If a person required to give evidence is already in the UK, IND [Immigration and Nationality Directorate] should be contacted at an early stage of court preparations, so that the person’s immigration status can be established. A person who meets the requirements of the Immigration Rules may be granted a short extension of stay. All applications to IND for an extension of stay will be subject to the appropriate fee1 and supporting evidence produced from the Crown Prosecution Service. Application Form FLR (O) should be used... This has since been withdrawn and replaced by form FLR(HTO)
A person already present in the UK but who is subject to removal action (for example as an illegal entrant), may be allowed to remain either in order to assist with investigations of serious crime or to be a witness for the Crown in a criminal prosecution. It is imperative that their immigration status is clarified and resolved at an early stage in order that the possibility of any allegation of inducement or favour regarding their immigration status is addressed.
I have not been able to find any publicly available sources on the internet, but I am led to believe that she would be issued with an "Immigration Document" within the meaning of section 7(1)(a), Identity Documents Act 2010.
This document may, depending on the particular circumstances, be a letter, a plastic "Residence Permit" card or some by other means to confirm Alice's temporary and discretionary leave to remain, and any restrictions that may be imposed.
1Depending on the particular circumstances any fees may be sourced from central funds, or she could apply for a fee waiver.