That is a true statement for any program that accepts input, strictly speaking. The halting problem is unsolvable.
The halting problem cannot be solved in general, but some programs can be proven to halt (or not halt). That's how the first few Busy Beaver numbers were found.
For something more substantial: a correct program that implements a regular language recognizer will always halt eventually on any input, because it always makes progress and doesn't have any nonterminating loops. It consumes the whole input and stops.
The hard part is proving you wrote it correctly, but that's what coq et al are for.
Analogous statements are true for programming in a dependently typed language.