12.11.2 Conjunctions of insecurity, fear and irreality quoi que + subjonctif = whatever ... may
Quoi qu' il dise, ils ne le croiront pas.
  Whatever he may say, they would not believe him.

quoi que + subjonctif (= whatever may) should not be mixed with quoique + subjonctif (= although, see chapter de peur que / de crainte que = for fear (with subjonctif)
Il ne voyage jamais de peur qu' il puisse lui arriver un accident.
  He never travels for fear of an accident could happen to him.

Please note that the subjonctif is used here, because the subject of the main phrase and the subordinate phrase are different. If the subjects are the same the construction with de (de peur de / de crainte de) is formed with the infinitive.

Il ne voyage jamais, de peur d' être agressé.
He never travels for fear of being attacked.

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