This isn't a weird state. It's a language problem. An 'incomplete line' isn't a type of line, it's an unfortunate name for a thing that is not a line. Just like how the 'wor' is an incomplete word (the word 'word'), but 'wor' is, of course, not a word.
Same thing for formalisms like equations in algebra or formulas in propositional logic— we have the phrase 'well-formed formula', and we might describe some sequences of terms as 'incomplete formulas' or perhaps 'ill-formed formulas', but those phrases don't describe anything that meets the formal system's definition of 'formula' at all— they are not formulas. 'Ill-formed formula' is not a compositional phrase where 'ill-formed' describes a feature of a 'formula'. It's a bit of convenient language for what we can intuitively or metaphorically recognize as a formula-ish thing.
This isn't a weird state. It's a language problem. An 'incomplete line' isn't a type of line, it's an unfortunate name for a thing that is not a line. Just like how the 'wor' is an incomplete word (the word 'word'), but 'wor' is, of course, not a word.
Same thing for formalisms like equations in algebra or formulas in propositional logic— we have the phrase 'well-formed formula', and we might describe some sequences of terms as 'incomplete formulas' or perhaps 'ill-formed formulas', but those phrases don't describe anything that meets the formal system's definition of 'formula' at all— they are not formulas. 'Ill-formed formula' is not a compositional phrase where 'ill-formed' describes a feature of a 'formula'. It's a bit of convenient language for what we can intuitively or metaphorically recognize as a formula-ish thing.