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I've heard that improving passive static flexibility is only possible for children, but for adults it's more or less set in stone, because it's not possible to lengthen the ligaments as you age.
So by this logic it's hopeless for an adult with average and below-average flexibility to try to do a split.
Are there any studies that would confirm or deny these claims? If it's not true, what kind of exercises can improve passive static flexibility in adults?
With work, you can improve your static-passive flexibility at any age. However, the gains you will see in time will significantly decrease as your age increases: the older you get, the harder it is to gain flexibility. Stating that it's impossible would be entirely incorrect, though.
See the "How Aging Effects Flexibility" section of Stretching and Flexibility - Flexibility by Brad Appleton for some of the scientific reasons behind this.
I don't have research that specifically addresses static passive flexibility, but I have this from Thomas Kurz' Stretching Scientifically:
The meaty, scientific evidence comes on page 27:
Past maturity both flexibility and strength decline, partly due to aging and partly due to inactivity. (Bassey et al. 1989, Gersten 1991; James and Parker 1989). Strength and flexibility training can decrease the age-related loss of strength and maintain or restore flexibility (American College of Sports Medicine Position Stand 1998; Buckwalter 1997). Strength training alone, without any stretching--with resistance permitting maximally 6-10 repetitions without straining, at a full range of motion--can increase flexibility of the elderly (Barbosa et al. 2002).
Even elderly men and women over seventy years old can increase their flexibility (Brown et al. 2000; Lazowski et al. 1999). With strength training the elderly, even in their 90s, can increase their strength and muscle mass--not as fast and as much as young people, but they can (Fiatarone et al 1990; Lexell et al. 1995)
And on page 126, he addresses a question from someone in their 30s asking just about the same question you're asking. Here's Kurz's response:
As long as your muscles are responsive to strength training (you feel they are getting stronger), they are also responsive to stretching. We have plenty of testimonials from people past their 30s saying and showing that they just achieved a side split.
So go forth and get that split.
I haven't read any studies saying that's an issue and I would be interested in seeing one if anyone has encountered them.
As far as exercise, I found that yoga greatly helped me improve flexibility (dynamic and static - active/passive).
