What is the sign, used in documentation, that means illegible--in the same fashion as [sic]?

From the U.S. Library of Congress:

Illegible or unclear text:

Illegible text is anything you can’t read because a page is damaged, text is heavily crossed out or because you can’t tell what the author has written. If there is a word or a string of words you cannot read use a pair of square brackets around a question mark [?]. Example:

"I have [?] loved coffee ice cream"

If you can read any letters or parts of words transcribe what you can and use question marks for the remaining letters or words. Examples:

"I have [a?????] loved coffee ice cream"

If you cannot read a word or phrase that’s ok. Another volunteer may be able to identify the missing letters and update your transcription. If there is a lot of text you cannot read consider saving your transcription and looking for another page that you can decipher better.

Other organizations may have different conventions. You may need to look into the policies and procedures of a specific organization.

The Chicago Manual of Style, 16th edition, lists 3 possibilities: ellipsis points, bracketed comments or guesses (frequently with a question mark), or a 2-em dash.

13.57 Missing or illegible words. In reproducing or quoting from a document in which certain words are missing or illegible, an author may use ellipsis points, a bracketed comment or guess (sometimes followed by a question mark), or both. If ellipsis points alone are used (useful for a passage with more than a few lacunae), their function as a stand-in for missing or illegible words must be explained in the text or in a note.

[Examples given]

If you will assure me of your ... [illegible], I shall dedicate my life to your endeavor.

She marched out of the door and headed straight for the [president's?] office.

A 2-em dash sometimes in combination with an interpolated guess, may also be used for missing material.

I have great marvel that ye will so soon incline to every man his device and [counsel and ---- ]specially in matters of small impor[tance ---- ] yea, and as [it is] reported [unto me ---- ] causes as meseemeth th[a---- ] nothing to [ ----]ne gentlewomen.

Notice the spacing around the 2-em dashes to indicate where in the word legibility occurred.