The government says benefit claimants and pensioners without a bank account can contact it about a payment exception service.
The current MiCard payment system will be scrapped on December 31 to save £500,000 a year.
Around two-thirds of claimants have already arranged to switch to being paid directly into accounts.
But the Treasury says a payment exception service will be available for those who can't receive such payments, and is urging people to contact the Social Security team as soon as possible.
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