Wolverhampton council is owed more than £10 million in outstanding council tax and has to save £134 million over five years, with 2,000 jobs going.
Figures released under the Freedom of Information Act show that the authority is owed funds dating back at least six years.
The council is owed £1,647,572 from before 2009, £632,557 from 2010/11, £783,426 from 2011/12, £963,033 from 2012/13, £1,807,310 from 2013/14 and £3,682,184 from 2014/15.
But of last year's debt, £91,600 has now been written off as bosses accept they have no way to recover it.
Councillor Andrew Johnson, cabinet member for resources, said: "The majority of people pay their council tax on time – as demonstrated by the fact we collected 95 per cent of monies owed during the last financial year.
"For the minority of people who don't pay, we rigorously pursue the debt using all legal powers at our disposal which includes court action, deductions from earnings and benefits and enforcement agents.
"We continue to pursue non-payers for as long as it takes and because of this we anticipate that last year's 95 per cent collection rate will become 99 per cent. We never write off a council tax debt until we are convinced a sum in truly unrecoverable – such as when a person dies leaving no estate or rare cases where an absconder cannot be traced.
"All uncollected council tax debt prior to 2012/2013 stands at less than 0.1 per cent, for 2012/2013 itself we have 1.2 per cent left to collect and for 2013/14 it currently stands at 2.2 per cent.
"Last November, the council approved a policy to impose fines on people who do not respond to requests for council tax information – such as when we check how many people live in a household. The first information canvass since this policy was approved is scheduled to take place this month and people who do not respond could face a penalty."
But Jonathan Isaby, chief executive of the Tax Payers Alliance, was critical of the council's decision to write off some of the council tax debt.
He said: "Questions must be asked about these council tax write-offs and whether more could have been done. The council has an obligation to ensure everybody pays what they owe – it's only fair on those who willingly pay up on time. There may well be good reasons, but we must learn the right lessons so that in future we don't have to go through this write-off process again."