First most of the time there's no "missing text", there's an empty string (0 sentences, 0 words) and this is a valid text value. The distinction is important, because the former usually means that the information was not captured whereas the latter means that the information was intentionally left blank. For example a user not entering a review is not missing information: the user chose not to enter any text and it cannot be assumed that this choice is equivalent to whatever text is the most common.
To the best of my knowledge there's no imputing in NLP. Imputing can make sense in some cases with a numerical value (even then it should be used cautiously), but in general text is too diverse (unstructured data) for the concept of "most frequent text" to make any sense. In general substituting real text (or absence of text) with artificially generated data is frowned upon from the point of view of evaluation.
Thus in my opinion the main design options are the following:
- Leave the text empty. Most of the time an empty text can be represented like any other text value, e.g. as a TFIDF vector made of zeros.
- Discard instances which have no text. For example in text classification no text means no input data at all, so there's no point performing the task for such cases.
- Treating instances with no text as special cases based on the specifics of the task. For example such instances could be systematically assigned the majority class, if that makes sense for the task.