For example, which is correct:
Плохие люди уже близко! or Плохие люди уже близки!
Also, would be helpful to understand the logic behind the adverb being used (if using the adverb is correct, that is.)
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"Плохие люди уже близко" will sound tiny tad more natural compared to "плохие люди уже близки", and here's why.
Technically both forms are acceptable here. When you are using first form, you are sort of speaking about the fact that bad people are not that far around, with "близко" being not some immanent property of bad people but a mere statement, an estimate of distance, so it's люди (как далеко?) близко.
When you are using the second one, you are talking about proximity as of attribute of the "bad people", you know, sort of like "люди (каковы?) близки".
In many situations this two words are interchangeable, but still, not quite always. Compare following two sentences:
If you'll leave just "мы уже близки" and "мы уже близко" and ask Russian native speaker to continue the sentence, in first case you most likely get statements about assessment of state, of how close we to some logical phase; while in second - description of physical proximity.
Just to make it clearer, compare following almost identical phrases:
First will be perceived by native speaker with a failure (so, "we are close to failure"), second one - with being literally close to abyss.
Here you shall use the adverb only (or so called short adjective близок, not form близкий). Плохие люди уже близки :> "The evil people is near yet".
"Плохие люди уже близко! or Плохие люди уже близки!" - the both forms are correct. 1 - "people as event", 2 - "plural objects, these people".
"близко-близкий" It's some complicated case here. :) The adjective "близкие, близкий" have got a connotation about "familiarity, intimacy, similarity"; not only about a physical distance between objects.
In this case this connotation, of course, is achieving full forse of it. But if you say just "ЭТИ люди близки" it mean "these people are familiar, etc" (but it depend on context :> In general, "Эти люди уже близки" can be meaning "these people are locating near" too :> In the some contexts the "Плохие люди уже близки" might be mean something like "these evil people had a sex, or have other intimate relations or friendship" yet )
"Плохие люди - близкие" - sounds as a grammar mistake or a semantic (or moral, mb.) brain-twister .
"Плохие люди близки друг другу" - sounds good, and it's about "familiarity-similarity".
"Это - близкие люди" sounds good, it's about "familiarity,etc".
"Эти объекты - близкие"... hmm... there isn't enough additional information here, it seems to me.
"Раздалась близкая стрельба" - sounds good, and it's about "distance"
"Это близкий мне человек " - sounds good, and it's about "familiarity,etc".
P.S. Additionally, these "Плохие люди" sounds somehow childly.
As other people said, the use of adjective may mean similarity or familiarity in addition to distance, which may be not what you would want to express. As in English "Those bad people are already close [to each other]".
Also, близко somehow implies approaching direction with eventual encounter, while близки implies approaching direction to a lesser extent.
Another difference, adverb implies "reachable", while adjective may imply physical closeness without being reachable. For instance, "Город находится близко от станции" - the city is close to the station (it is easily reachable), while "Город близок к станции" - may imply the city is near the station, but there is some obstacle that may make it unreachable (state border, river, swamp, etc) There is a Russian proverb, "Близок локоть, да не укусишь" - "The elbow is close, but you cannot bite it"