Display posts with empty custom field

You probably need the NOT EXISTS meta_compare value. This will test if a meta value exists or not for that particular key.

Also, as I pointed out in comments, caller_get_posts is long time deprecated, a notice you should have clearly recieved if you had debubbing turned on. The correct parameter is ignore_sticky_posts and accepts 0 (false) or 1 (true)

EDIT

One issue I missed is, value should be meta_value when not using a proper meta_query

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