SEOUL, South Korea — In late 2014, months after 304 people died in the sinking of a South Korean ferry, a leaflet began circulating with a scurrilous rumor about President Park Geun-hye: that she had failed to respond swiftly to the disaster that day because she was having a romantic encounter with a former aide.

Was Ms. Park, the flier asked, now cracking down on her critics in an attempt to keep that scandal from coming to light?

For Park Sung-su, an antigovernment campaigner who had distributed the leaflet — and who is not related to the president (Park is a common surname here) — the consequences soon followed. He was arrested and later sentenced to a year in prison, on charges of defaming the president and staging illegal protests against his prosecutors. He was freed in December after eight months, when a court suspended his sentence.

No evidence supporting the rumor has been produced, and prosecutors said they had investigated and found it groundless. But however dubious the leaflet might have been, opponents of the government say Mr. Park became another victim of the very thing he was denouncing: the government’s use of defamation and other laws to silence its critics, which rights advocates say is on the rise.