She has indefinite right to remain. If she wishes she can have a British passport, she may well have oe already
Government has said all EU citizens can stay for the time being at least, they would only be asked to leave if EU threw out British citizens which frankly would be petty madness. If you are an EU citiznnhere legally its almost certain you could stay 7 years and get a British passport, this does create problms with some nationalities like the Dutch and their government does not allow two EU passports.
#Jambafact
She doesn’t have indefinite leave to remain. She has no need for that if she is an EU citizen and thus the home office wouldn’t grant it for an EU citizen. If she had been granted it (as a non-EU citizen) it is “for life” and can’t be revoked as a tit-for-tat under diplomatic disputes.
The rule for EU citizens applying to be british passport holders / citizens (subjects) is 5 yrs not 7 (and I think it might be 3 for spouses of UK citizens). BUT requires them to pass a citizenship test and language test; has reasonably tough residence requirements (which if she travels with Nigel on his EU parliament meetings she may not meet)…