Fairfax City residents packed the courtroom last week, as their former treasurer, Frances L. Cox, went on trial for embezzlement of city funds. Some were old political friends of the former city official. Others came out of curiosity. And some were angry, outraged.

"It causes you to lose a lot of faith in your elected officials," said Fairfax City Mayor John W. Russell, who observed several hours of the court proceedings. "It's a hard thing to face. You feel let down. Naturally, the citizens' faith in their government is a little shaken."

A Fairfax Circuit Court jury found Cox guilty of embezzling an unspecified amount of money from city accounts during a 30-month period ending in December 1981. At the trial, prosecutors said $200,000 in cash Cox deposited in her personal bank accounts was believed to be the "minimum" loss to the city. City officials now say that may be only a fraction of the money missing from city accounts.

Cox's attorney argued throughout the trial that the woman who served as city treasurer for 27 years may have been incompetent but was not dishonest.

"Mrs. Cox is a politician, she's not an accountant," her attorney, John H. Rust Jr., said at the trial. "She started out in a small town and . . . the town grew up around her. Maybe she didn't adjust to the sophisticated, cosmopolitan techniques of accounting now required for the city."

That argument may rekindle a years-old political controversy over local elected positions that are given the power by the Virginia Constitution to collect local and state taxes. In Fairfax City, where the treasurer's post has been an elective position for 21 years, Russell said, "I expect people to come forward and push for making the treasurer's job an appointed office."

Although most counties and cities in Virginia have maintained a system of elected treasurers and commissioners of revenue, several larger jurisdictions -- including Fairfax and Prince William counties and Alexandria -- have scrapped some of the elective constitutional officials for appointed professionals.

Some critics also have argued that the elective system creates friction among the elected officials, appointed staff members and the elected city council members who have little, if any, control over the elected treasurer and commissioner of revenue.

"An elected treasurer isn't accountable to anyone except the voters," said one Fairfax City official.

In Fairfax City, residents and the City Council had been warned intermittently since 1965 that something was amiss in the treasurer's office.

Auditors discovered an $826 deficiency in state tax funds handled by the city treasurer's office in 1965. Cox blamed the lost funds on clerical errors by inexperienced employes, and paid the amount, she said, from her own pocket.

By 1979 the discrepancies in the Fairfax City accounts had grown to about $48,000, auditors reported. Similar amounts were listed as "misclassified" in 1980 and 1981. With each report, auditors said "there is no evidence of wrongdoing," but warned that Cox's sloppy record-keeping practices could leave the door open to theft.

Cox continued to blame the problems on clerical errors and an inexperienced staff. For the most part, city officials and voters accepted her explanations.

"You'd be amazed at how simple it the scheme was," said Deputy Commonwealth's Attorney Steven Merril during the trial. "It required only one thing -- that she stay in office."

Voters continued to return Cox to office and the City Council never gave her more than verbal reprimands year after year. Until last year, that is. Cox's opponents, armed with the official audit reports, campaigned hard against what they termed her incompetence as treasurer. Cox replied by accusing them of misrepresenting the comments of auditors.

But the opposition was successful, and Ray M. Birch was elected city treasurer. He quit after three weeks in office, however, saying Cox had left the office in complete disarray with cash stuffed in desk drawers, checks left unrecorded and a $156,000 overdraft on the city's bank account.

Former Fairfax City mayor Frederick W. Silverthorne said it would be unfair to abolish the elected position on the basis of the Cox scandal.

"There's nothing wrong with the constitutional officer system," said Silverthorne, who was mayor during the period Cox was charged with carrying out her embezzlement scheme. "If you get a crook in there, he's going to rob. If the council had been on the ball, it would have been a big help."

Testimony in the Cox trial raised another disturbing issue: the annual audits of most political offices and government agencies aren't designed to detect fraud. Auditors testified that they seldom account for every cent of money in any audit. In fact, auditors testified, they don't even consider any discrepancy above 3 to 5 percent of the total budget as "significant." In Fairfax City, with an annual budget of about $25 million budget that could mean thousands of dollars in misplaced funds would not be considered a major discrepancy by auditors.

Fairfax City residents learned during the trial that the city spent as much as $25,000 extra on annual audits because Cox's records were in such disarray.

Now Fairfax City is drawing up, for the first time, policies governing the operation of city financial offices. It sets up a system of checks and balances between the treasurer's office, commissioner of revenue, real estate tax collections and data processing system.

Fairfax City, said one local official, learned an expensive lesson.