WWWJDIC states that 「だらしない」 can be written with kanji as 「だらし無い」, which suggests that the phrase is a negative construction that uses 「無い」, unlike words like 「すくない」 and 「あぶない」. Furthermore, 「だらしが無い」 and 「だらしの無い」 are listed as the other two variants of the phrase, which imply that the phrase is using 「だらし」 as a noun, instead of being derived from the negative of non-existent verb 「だらしる」. However there is no dictionary entry on 「だらし」 other than as "dalasi", the currency of the country of Gambia, and "だらしない" variants.
So, what exactly is 「だらし」? Or was there a verb 「だらしる」 which is now extinct?