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Not at all, it is your employers responsibility to pay the sums deducted to HMRC. Failure so to do cannot create a liability on your part.
You can apply to the DWP.
Have a look here for details:
Useful telephone numbers for the Department for Work and Pensions (DWP) - CASS The Carers Association (carersinformation.org.uk)
Delighted to have been of assistance.