"rife" means something is common. For example, "the airport is rife with weary travelers." For something to "run rife" typically means something is becoming common or is spreading. For example, "Once the lockdown ended, covid ran rife through the close-knit community." The usage of this term is not very common and may be a little subtle. One wouldn't say, for instance, "the usage of this term of not rife."

hello run rife = "to spread quickly, in an uncontrolled way." the thing is, run can mean "become" and rife can mean "most frequent or common", so, logically speaking "run rife" could mean "become the most common", but they don't use it like that.

Not quite. "Run rife" means that something is uncontrolled. For instance, in an area where crime is rampant, one could say "burglars run rife around here". If children are misbehaving at a party one could say "the children were running rife at the party". It doesn't necessarily mean something is common or multiple either, because one person can "run rife", like "Jack the Ripper ran rife around London". Also it isn't a very common expression these days.

mistakenly commented instead of "answered." Disregard comment.