A family of Microsoft word processing software products for creating web, email, and print documents.
Assuming you're using a dropdown content control and not a legacy formfield:
Apply a style to the paragraph that contains the dropdown, making sure that style isn't used anywhere else in the document. If necessary, create a new custom style for this purpose.
Then insert a StyleRef field in the footer, including the name of the style in the field's code. The field will automatically update to display whatever is in the styled paragraph, including what is chosen in the dropdown.