What are derivative rights
Home Office guidance "Free movement rights: derivative rights of residence" (I need to link to document) states:
" 'Derivative rights' are rights which come from (or are 'derived' from) other instruments of EU law rather than from the Free Movement Directive 2004/38/EC (the Free Movement Directive). A person who is not an ‘exempt person’ may qualify for a derivative right of residence. The requirements are set out in regulation 16 of the Immigration (European Economic Area) Regulations 2016 (the 2016 regulations).
An ‘exempt person’ is defined in regulation 16(7)(c) of the 2016 regulations as a person:
• who has a right to reside in the UK as a result of any other provision of the 2016 regulations, for example, a person who is already exercising free movement rights as a European Economic Area (EEA) national • who has a right of abode in the UK by virtue of section 2 of the Immigration Act 1971 (the 1971 act), for example, the person is a British citizen
• to whom section 8 of the 1971 act, or any order made under subsection (2) of that provision applies • who has indefinite leave to enter or remain in the UK"
Derivative Rights - initial rules:
But non EEA nationals whose right to reside is only through a derivative right will not be able to apply for 'settled status' under the EU Settlement scheme*- see below. However it appears they will have their rights to benefits protected while they keep their derivative right: according to the Statement of Intent:
"The ..derivative residence rights of primary carers (of EU national children in education) will be protected for as long as the child requires the primary carer's presence to continue or complete their education".
We assume what this means is that once they lose the derivative right, eg when the child leaves education they will lose their right to claim benefits.
However it appears that, while they have the derivative right, they will be able to apply for an immigration status that might allow them to claim benefits: a government statement on May 16th 2018 stated:
"...provision will be made for them elsewhere in the Immigration Rules to apply for leave to remain in line with their current rights."
* From a Parliamentary report
... Ibrahim & Teixeira Rights
Children of former EU citizen or UK national workers who are in education in the UK or the EU will be able to remain to complete their education (Ibrahim & Teixeira rights). The associated derivative residence rights of their primary carers will be protected for as long as the child requires the primary carer’s presence to continue or complete their education.
Some of these persons.... will be EU citizens eligible to apply for status under the settlement scheme. Otherwise,(ie not themselves EU nationals) provision will be made for them elsewhere in the Immigration Rules to apply for leave to remain in line with their current rights. As their current rights do not lead to a right of permanent residence under EU law, they will not be able to apply on the basis of those rights for status under the settlement scheme.
After any leave to remain granted on the basis of ... Ibrahim and Teixeira status expires, and if the person does not qualify for further leave on that basis, they may wish to apply to remain in the UK on an alternative basis, if they meet the requirements of another category of the Immigration Rules.