Firstly, your client seems to have been refused IS not because she has been held to be a "Person Subject To Immigration Control" (PSIC), but as she hasn't got a NI Number.
There is a useful CPAG briefing on the need for NI numbers available in swopshop:
National insurance number problems
In addition, as she is a Polish national, although she would seem to be a PSIC, she would be able to access IS on the basis she is "lawfully present" here (see the rightsnet Q&A: Which people "subject to immigration control" can access Income Support, income- based JSA, Pension Credit, HB/CTB? Its not clear from your posting what kind of leave to remain she has, but if she has sought to extend her leave within 28 days of her present leave expiring, she should be OK (see R(DLA)1/01 on "variation of leave")
However, she may need to get confirmation from her solicitor that this has been done, and should get their advice as to how any IS claim may her affect her future ability to remain in the UK.
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