I don't know what kind of malnourishment you are talking about, but in the case of anorexia-related osteoporosis, there is a with osteoporotic fracture as mentioned in the introduction of "Factors Influencing Changes in Bone Mineral Density in Patients with Anorexia Nervosa-Related Osteoporosis: The Effect of Hormone Replacement Therapy. Legroux-Gerot et al, Calcif Tissue Int (2008) 83:315–323 :

Over the last few years anorexia nervosa (AN) has become a serious public health issue in industrialized countries. AN occurs with a very high frequency among young women (0.5% prevalence as opposed to 2% for bulimia) and gives rise to serious metabolic complications resulting from malnutrition [1, 2]. One of the complications of the disorder is bone loss. Indeed, osteoporosis may occur in 20–50% of cases depending on the groups observed, with bone fracturing occurring in 44% of patients [1–7]. In patients who have had the disorder for an average of 5.8 years, the risk of fractures occurring is seven times higher than in healthy women of the same age [8]. Fractures tend to occurat the most common osteoporotic fracture sites, i.e., most frequently at vertebrae and at the radius and the upper extremity of the femur [3, 9–11].

I hope this will contribute to answer your question.

I think exact factors that determine bone mineral density are poorly understood but studies in twins indicate that  the BMD is determined by heredity . Other important factors are environmental factors such as the level of estrogen, testosterone, and growth hormone in addition to the level of exercise and nutrition as well as any diseases that interfere with normal growth. but i don`t know that is there any direct correlation between osteoprosis and protein-energy malnutriyion.

best regards

It is evident that dietary deficit in development period has negativy  influence for  achieving a good bone mass, which facilitates the appearance of osteoporosis and fractures result. In adulthood also has importance insufficient or unbalanced feeding in the appearance of osteoporosis . The malnourishment is one of the risk factors that are valued in the appearance of osteoporotic fractures

The quality of bone, at the age the peak bone mass is achieved, is dependent on vitamin D, K status and calcium metabolism during growing (bone modelling). At menopause osteoporosis is affectig one in three women. In this incidence a major role plays the genetic inheritance (about 70%). The rest of two from three postmenopausal women, who are not affected by osteoporosis, may develop osteopenia in vitamin D and K deficiency (as well nutritional deficiencies), but I do not know any study showing the risk of fracture in osteopenic subjects.

Malnutrition, such as vitamin D and/or calcium deficiency, might also trigger hyperparathyroidism which will eventually cause osteoporosis. Besides factors such as age, sex and genetics, the nutritional quality of diet should be considered.

I agree with Dr. Chauveau and Dr. Herrera that poor supply with calcium rich food can conntribute to osteoporosis by disturbing calcium metabolism. On the other hand,this is the idea of treating osteoporosis with biphosphonaytes,calcium (obligatory) and vitamin D.

 As previously said there most be a link,  it sound logical than Vit. D and Calcium Deficiency are related, but other factor my have a role to, we made a study about Hip surgery and delay healing in nutritional deficiency using the lymphocyte count(less than 1500) as a parameter, it doesn't need special studies and have been used as marker in other pathologies as Pneumonia risk in Elderly, we found 26 of 48 patient with low lymphocyte count but no difference between traumatic or non traumatic surgery. 

 As we have seen we can not explain Fracture Risk only  with the mineral part of the bone and it appears that proteins of the extra-cellular matrix play an important role, so i Will go for protein Deficiency in firs place.

Hope it serves

 This is the link to the article although is in Spanish.

Article [Malnutrition and osteoporosis]

Yes, severe malnutrition can lead to vitamin D and Calcium deficiency, and these in-turn can lead to osteoporosis