A council officer said he has been unable to proactively investigate fraud because his team was down to just two people.
But Jonathon Rogers told Swansea's audit committee that fraud nowadays came "looking for us".
Mr Rogers has set out written details of anti-fraud activity his team planned to undertake during the current financial year.
These include proactive work on procurement and social care payments, subject to available resources.
The team, which had three officers last year, will also work jointly with the council's housing department to tackle tenancy fraud, such as illegal sub-letting.
And it will team up with the Department for Work and Pensions at the end of this month to investigate council tax fraud.
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Mr Rogers said: "We've spent the year being completely reactive in terms of our work.
"We can write our plan, and say what we're going to do - but whether we are able to do it, we don't know."
The previous year the team helped save nearly £300,000 of over-claimed housing benefit, council tax reduction and other state payments.
They also investigated reports of in-house fraud involving 35 council employees, with a further 15 brought forward from the previous year.
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Councillor Peter Black said he wanted to know more about the impact of having a two-person team and whether this had been risk assessed.
Mr Rogers said this might become clearer when the team provided full details of the cases investigated during 2018-19, compared to the previous year.
"The proof of the pudding will be when we present the full report in the summer," he said.
But he added: "We don't have to look for fraud at the moment - it's looking for us."
Committee chairwoman Paula O'Connor, who is not a councillor, said: "We look forward to seeing the position in the summer as a comparison."
