She could claim ESA if the meets the usual (WCA) conditions, but if she falls into that limbo where she is not ill or disabled enough to get ESA, she can still restrict her availability to 16 hrs.
Regulation 13(1) and (3) of the Jobseekers Allowance Regulations 1996 SI 1996 no 207 as amended provides:
13.—(1) In any week a person may restrict his availability for employment in the following ways, if the circumstances set out apply.
(3) A person may restrict his availability in any way providing the restrictions are reasonable in the light of his physical or mental condition
The provision is not strictly speaking discretionary but permissive. The question is simply a judgement call as to what is reasonable..
This is tempered somewhat by Regulation 10 which provides
Reasonable prospects of employment
10.—(1) For the purposes of regulations 7 and 8 and paragraphs (2) and (4) of regulation 13, in deciding whether a person has reasonable prospects of securing employment, regard shall be had, in particular, to the following matters–
(a) his skills, qualifications and experience;
(b) the type and number of vacancies within daily travelling distance from his home;
(c) the length of time for which he has been unemployed;
(d) the job applications which he has made and their outcome;
(e) if he wishes to place restrictions on the nature of the employment for which he is available, whether he is willing to move home to take up employment.
(2) It shall be for the claimant to show that he has reasonable prospects of securing employment if he wishes to restrict his availability in accordance with regulation 7 or 8 or paragraph (2) or (4) of regulation 13.
In CJSA/ 4435/1998 Mr Commissioner (as then was) Levenson considered how a claimant could show that he had reasonable prospects of securing employment when he had restricted his availability