This is the step this route exists for above all. The word invitation sounds hospitable; what gets signed is an enforceable money debt.
Two figures nobody mentions
The scope. Not board and lodging but all public funds spent on subsistence — including housing, illness and long-term care, and even where your guest has a statutory entitlement to them.
The duration: five years from entry. Not until departure, not until the visa expires. A three-week visit creates a bond that outlasts half a childhood at nursery.
The sentence worth knowing before you sign
§ 68 (1) sentence 4 AufenthG states expressly that within those five years the declaration does not lapse through a humanitarian residence permit and not through a grant of international protection.
That is no edge case; it is the reason the sentence exists. These are exactly the situations in which public funds flow.
Anyone who knows this signs differently — not necessarily less often, but with open eyes.