The city council wants to get people's views about plans to reduce the assistance given to people on low incomes - known as Council Tax Reduction - by 10%.
At the moment, the maximum support a low income household is given towards their council tax covers 88% of the total bill.
The council is proposing to reduce that support by 10%, meaning the new maximum figure for Council Tax Reduction would be 78% of the total bill. That would mean households on low incomes would have to make a larger contribution towards their council tax.
The proposal would not affect pensioners who get support towards their council tax bills. Pensioners will continue to receive the same level of support as before.
Councillor Andrew Johnson, the council's cabinet member for resources, said the proposal was being put forward as the local authority continued to face huge cuts in Central Government funding.
He said: "When the Council Tax Reduction scheme was introduced, we suffered a 10% cut in Government support from the very start. For the last 2 years we've done our best to protect vulnerable people from this shortfall.
"With sustained Government cuts continuing and a predicted funding gap of £123 million for services by 2018/2019, we have no choice but to make additional changes to the scheme.
"Before we make any final decisions, we are giving every household in the city the chance to comment on the proposals. This is not a cosmetic exercise, we genuinely want to know what people think. Last year, as a result of feedback, we made changes to our plans - in particular people with savings up to £6,000 were protected from losing their support."
The consultation is open until 31 October and there are a number of ways for people to get involved.
Each household will receive a booklet through the post which explains the proposed changes and contains a questionnaire that can be sent back.
Alternatively, people can complete the confidential survey online via Type=links;Linkid=3978;Title=Council Tax Reduction Scheme 2015/16;Target=_blank;.
People can also visit roadshows being organised by the council which take place as follows:
Central Library - 9 September, 9am to 1pm
Wednesfield Market - 16 September, 9am to 1pm
Bilston Market - 18 September, 9am to 1pm
Wolverhampton Market - 23 September, 9am to 1pm
Tettenhall Library - 25 September, 10am to 1pm
- released: Monday 18 August, 2014