I would say "for people to continue the unfinished work of the soldiers"
treating serious issues with deliberately inappropriate humor; flippant.
The term <em>slang</em> refers to <u>informal language</u> and it is usually considered to carry negative connotation, because it stands out from the standard, formal language.
So the answer here is that the connotation of <em>slang</em> in the second sentence is that:
The word <u>legitimate</u> helps us understand this, that even though slang was considered a bad thing, through time those words gained full meaning and are now commonly used.
They're impersonal and know everything about the story