> field:"value" OR (*:* AND NOT field:[* TO *])
> 
> Which means, either field is set to "value" or the field
> does not exist in
> the document.

Instead of field:[* TO *], you can define a default value in schema.xml. Or 
DefaultValueUpdateProcessorFactory in solrconfig.

With this, "the field does not exist in the document" part becomes 
field:MySpecialDefaultValue

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