A mixture of "financial instability" among care companies and a shortage of nurses has sparked fears that vulnerable adults in the district may be left without adequate help or a home.
The council's director for adults and health, Andrew Balchin, said in April this year that some private providers were abandoning the north of England, and moving south where they believe they can make more money.
It means there are now potentially fewer places in Wakefield for elderly and disabled people to go if they need round-the-clock help, and the financial and logistical responsibility for their care ultimately belongs to the council.
A report prepared for councillors rated a number of issues on a scale of one to 25. The higher the number indicated the greater the risk to the council's "ability to operate" and "achieve its strategic objectives".
While exiting the EU produced a current score of six, the failure of private care providers was given a score of 15.
The report said this is, "due to financial instability of care providers, inadequate planning, business failure of a service provider and lack of nursing provision by
It added: "There is a risk of failure to commission adequate hours and placements of care to meet statutory need.
"This may result in unmet need, potentially putting vulnerable people at risk and poor outcomes for service users."
The council says it has taken several steps to mitigate the damage of a care provider collapsing, including reviewing its "contractual options" and increasing capacity where it can.
On Brexit, the report said that there "may be a degree of potential disruption which may impact on council services and residents" if the UK leaves the EU without a deal.
However, it added that extensive preparations for such an event have helped mitigate against the risks, though it acknowledged that the effects are "outside the control" of the local authority.
The report will go before the council's audit committee next week.
Local Democracy Reporting Service