BRUSSELS — The former mayor of Brussels has vanished.

On Thursday night, the mayor, Yvan Mayeur, offered his resignation at a tumultuous City Council meeting, hours after a government-ordered audit found that he had been paid 36,000 euros (about $40,000) over two years to attend board meetings of an agency that helps the homeless, even though there was no evidence such meetings took place.

Since then, Mr. Mayeur has been out of view. On Friday, Belgian journalists reported that he was meeting with colleagues about his political future in an undisclosed location. On Monday, hundreds of residents held a sit-in on the Grand Place in Brussels to demand that Mr. Mayeur address the city about its future. Tuesday came and went without any evident public statement by Mr. Mayeur, 57, who had been in power since 2013.

The bizarre resignation is only the latest of several corruption scandals that have ensnared politicians and sowed doubt about the health of democracy in Belgium, a country where power is divided along regional and linguistic lines, and across multiple layers of government: federal, regional, communal, provincial and local. The country famously went 541 days without a functioning government after a June 2010 election in which no party gained dominance.

The complexity of governing in Belgium — which some critics have called the world’s wealthiest failed state — may create a welcoming environment for corruption. Even Mr. Mayeur’s job is hard to explain: He was mayor of the City of Brussels, which has a population of 178,552 and is one of the 19 municipalities that make up the Brussels capital region (population 1.2 million).