What you asking for is portrait photographs. There are type of portrait photographs too. Like Still photography is one of branch for it in which object has to be constant. Going back to your topic , yes it is very much possible to snap your pic without moving you. For that lot of photographers provide instruction sheet prior moving to photo shoot.
Most of studios camera, lights adjustments are already made.
But human nature is we don't read all instructions and simply get ready for photo. It is photographer duty to tell what you missed. E.g. Passport photos don't need smile with teeth visible, eyes open etc. if you don't follow this then photographer will prompt. This is situation of indoor shooting.
For outdoor shooting, only random portrait photos don't need any modification in object or human emotions. e.g. portrait of villagers, popular and great leaders, wedding events , wedding event guests etc. But during wedding , home ceremony like hose warming, baby shower everyone want different pose photos so technically photographer has to tell different poses they can do.
Light is most important part of photo. 99% photographers will carry flash camera or extra light reflectors. But in some cases adverse situations if camera flash don't help then photographers ask for adjustment like getting into place where is sun is from front side or light drops on face etc.
Eventually no photographer wants person to make movements for any reason. And yes photographer can take photos without moving you.
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