I am not in a position to advise regarding any surgical procedure (loosening of local ligaments, division of fascial support, or other) that might predispose anatomically  to vaginal prolapse but, once such a predisposition is established, the prolapse could be encouraged by raising the intra-abdominal pressure.

Workers in the Department of Physiology at St Thomas' Hospital Medical School were investigating the Valsalva manoeuvre in greyhounds during the 1970s and managed to increase intra-abdominal pressure by means of a small balloon inserted in  the rectum. When inflated this mimicked the presence of a faecal mass and induced 'straining at stool' with the desired raise in pressure.

Thank you so much Dr. Barlow.

some mammals have "natural" prolapse

cf. Yiou R, Delmas V. [Comparative anatomy of pelvic prolapses in humans and quadruped mammals] Prog Urol. 2005 Dec;15(6 Suppl 1):1334-7. Review.

Thanks a million.

This article is the most up to date reference regarding pelvic organ prolapse in animals. I think you may find it useful.

Article Animal models of female pelvic organ prolapse: Lessons learned