I said jokingly in conversation:

Tu me demandes des renseignements ? Et sans bourse délier, en plus ? Pourvu que je puisse au moins m'en jeter un à l’œil !

Looking back, I have always used this phrasing without thinking much about its odd construction, or more specifically, the placement of "bourse". I'd sooner expect the phrase to take the form of "sans délier ta bourse" or "sans la délier". I wonder how this word order is considered grammatical?

Grammatically, "sans bourse déliée" makes more sense. As far as the commonly employed usage is concerned, however, "sans bourse délier" seems significantly more popular. I recall seeing native speakers use this expression several times, and it was "sans bourse délier" each time.

Le Petit Robert, Wiktionnaire et j'en passe, à l'appui :

http://www.pourquois.com/expressions_langage/pourquoi-sans-bourse-delier-.html