Should false rape accusers be sued?

The short answer is yes.

From Roxanne Jones at CNN:

In 2012, according to the FBI, nearly 87,000 "forcible rapes" were reported. That's down 7% from the number of rapes reported in 2008. Law enforcement agencies estimate that the number of false rape accusations ranges from 2% to 8% annually, or between 2,000 and 7,000 cases each year.
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In 2002, Brian Banks was one of those unfortunate statistics. He was just 17 when a classmate, Wanetta Gibson, 15, falsely accused him of raping her at school. Banks, then a top football talent, spent more than five years in prison and five years on probation for rape and kidnapping.

He was exonerated after he got his accuser to admit on tape that she lied about the rape. Banks later explained that his attorney had advised him to take a plea bargain and avoid a jury trial because "... I was a big black teenager, and no jury would believe anything I said."

The Long Beach Unified School District sued his accuser, and she has been ordered to repay the $750,000 she was awarded in a lawsuit against the district.

And those women should be prosecuted as well. One could argue that if Crystal Mangum, the false Duke Lacrosse Rape "victim", was prosecuted, she would have been in jail. Instead she was free to stab her boyfriend to death.