A mother has called on Boris Johnson to provide support for those migrants who have been financially hit by coronavirus, but cannot claim benefits.
Speaking to BBC Radio 4, the woman said her family had lost more than 60% of their income but could not get support due to immigration rules.
Despite paying taxes for almost 17 years, she said her family were now unable to "fulfil our basic needs".
When questioned on the rules, the PM promised to see what the he could do.
The family's case was raised by Labour MP Stephen Timms during the PM's appearance at the Liaison Committee on Wednesday.
He explained the family had leave to remain, but said the husband had not been put on the job retention scheme and, although the wife was still working, her income was less than household rent - adding that they had no recourse to public funds.
"Isn't it wrong that a hard-working, law-abiding family like that is being forced by the current arrangements into destitution," he asked.
Mr Johnson initially appeared surprised that the couple could not claim Universal Credit and replied: "Clearly people who have worked hard for this country should have support of one kind or another."
He added: "I will find out how many [people] there are in that position and we will see what we can do."
Speaking to the BBC, the mother of the family - who wanted to remain anonymous - said she and her husband were "shocked when we heard the prime minister was unaware of the current situation of families".
She added: "For almost 17 years, we have been paying our taxes and contributing to economy without claiming a single benefit. Both my children were born here, both are British nationals, yet they are not entitled to any benefits due to our legal status.
"If the condition continues, we won't be able to pay rent, we won't be able to pay the bills. We have young children and I know so many other families are struggling with the same condition.
"I really, really would like for the prime minister to remove NRPF [no recourse to public funds] conditions."
NRPF status is given to some migrants as a condition of their leave to remain in the UK, and prevents them from receiving most government funded benefits.
Mr Timms - who is chair of the Work and Pensions Committee - has written to the prime minister asking him how many people in the UK have no recourse to public funds, how many children are affected and what support the government will offer to those in difficulty.
The Children's Society charity, which has been campaigning on the issue, estimated more than 100,000 children could be affected by the rules.
A government spokesperson said: "We have been clear that no one should find themselves destitute during this crisis due to circumstances beyond their control.
"We have taken action across the system to support those with no recourse to public funds, including protections from eviction for renters and mortgage holidays, as well as support through the Coronavirus Job Retention Scheme, Self Employed Income Support Scheme and those on zero-hours contracts.
"People granted leave under the family and human rights routes can also apply to have the conditions lifted if their financial circumstances have changed."