Britney Spears is liable to develop a line of clothing bearing her son's namesake, for she recently filed a trademark application for the words "SEAN PRESTON."
This sentence contains an error in diction: "liable" has been used in place of "likely."
"Liable" means "responsible," as in "Parents are liable for their children's behavior." It can also mean "probable," but only when it precedes an infinitive that would cause a negative outcome for the subject, as in "You are liable to fall if you walk on a wet floor" or "If he does not study, he will be liable to fail."
In this sentence, the infinitive is "to develop." While her endeavor may possibly fail, developing a line of clothing is not a negative outcome. It would be something that Britney planned and desired. A better word to use in this sentence is "likely," which means "probable" but without the negative connotations of "liable."
The sentence should be written as follows:
Britney Spears is likely to develop a line of clothing bearing her son's namesake, for she recently filed a trademark application for the words "SEAN PRESTON."