People who started jobs in March have been left "petrified" after discovering thousands are not eligible for government wage grants.
Chancellor Rishi Sunak outlined a scheme where companies could apply for a grant worth 80% of their employees' salaries - up to £2,500 a month.
But in order to qualify, workers would have had to start their new job by 28 February, meaning a significant number have fallen through the cracks.
Many have called the cut-off "unjust".
Companies are choosing to furlough staff as industries grind to a halt during the crisis, and support has been offered to people who are long-term self-employed.
But workers who began working at companies on or after 1 March will not be able to receive a government grant, and some have been forced to take unpaid leave.
Natalie Greenway left a job in retail management to start a new job as a customer services manager at a call centre on 16 March.
The 24-year-old, from Burbage in Leicestershire, said: "I got the call from my company saying 'we're so sorry, we can't furlough you'.
"They were really sympathetic and offered to keep me on the books unpaid so I could have a job to go back to.
"I'm staying on the books, I'm not entitled to jobseekers as I am employed."
One man from Halifax in West Yorkshire said he and his family are having to make ends meet on his partner's £140-a-week statutory maternity pay.
They have a three-month-old baby and were intending to get married in Gibraltar in May.
But he has gone on unpaid leave after starting his new job at a car parts logistics firm on 9 March.
He said: "My new employer's been really good, I've got assurances that I can go back to my role once things get back to normal, but there's no time frame."
"Thousands of families could be at risk of losing their home, and they could be at risk of not being able to feed their family.
"It's unjust, it doesn't feel true and fair."
He is also on immunosuppressant drugs for a pre-existing condition, and is limited to working from home.
They have now taken a three-month mortgage repayment holiday on their new home.
His partner said: "I'm petrified, the fact that we could lose our home and we've got a three-month-old baby."
Zoe Badder, from Penrith in Cumbria, was due to start a new administrative role at a solicitors on 23 March, but her start date has now been delayed.
The 26-year-old said: "I rent with my partner, and he is working but he's just been furloughed.
"We're not in as bad a situation as some people, but money is going to be very tight."
Her situation inspired the Twitter hashtag #newstarterfurlough, which has been used thousands of times.
More than 12,000 people have signed an online petition asking the government to amend the cut-off date.
Labour Shadow Chancellor John McDonnell has called on the government to include workers who started new jobs after 28 February.
CONFIRMED: If u left a job after 28 Feb, that old employer can rehire you to furlough u. So if needed ask.— Martin Lewis (@MartinSLewis) March 31, 2020
We knew this worked for those made redundant, but Treasury's just confirmed to us, this is allowed for those who left voluntarily (eg for a new job).
Tell those affected
According to finance expert Martin Lewis, some people can return to their old place of work to receive furlough payments.
"Sadly many employers won't do it," he said.
"However the fact it is confirmed to be legal and it can be done, may help persuade some."
A Treasury spokesman said: "Our Coronavirus Job Retention Scheme is protecting thousands of jobs up and down the UK - with the government covering 80% of the salary of furloughed workers.
"Firms can re-employ staff made redundant after 1 March and those who do not qualify will be able to access a range of other support - including an increase in the Universal Credit allowance, income tax deferrals, £1bn more support for renters and access to three-month mortgage holidays."