From the Guidelines

Calcium supplementation is useful in preventing osteoporosis in immobilized patients, but only when combined with vitamin D supplementation.

The combination of calcium and vitamin D supplementation has been shown to reduce the risk of fractures, particularly in older adults 1.
Calcium supplementation alone may not be effective in preventing fractures, and high doses may increase the risk of myocardial infarction 1.
The optimal dose of calcium supplementation is 1,000 to 1,200 mg per day, and vitamin D supplementation should be at least 800 IU per day 1.
Immobilized patients, such as those who are bedridden, are at higher risk of osteoporosis and fractures due to lack of weight-bearing exercise and mobility.
A study found that high-dose vitamin D supplementation (≥ 800 IU/d) reduces hip fracture and any nonvertebral fracture in persons age 65 years or older 1.

The USPSTF recommends that adults 65 years and older take vitamin D and calcium supplements to prevent fractures, but notes that the evidence is not strong enough to make a recommendation for younger adults 1.
The balance of benefits and harms of vitamin D and calcium supplementation cannot be determined for men and premenopausal women 1.
Patients should be counseled on the potential benefits and harms of calcium and vitamin D supplementation, including the risk of renal stones and myocardial infarction 1.

The FDA Drug Labels for calcium (PO) do not address this question.

From the Research

The usefulness of calcium supplementation in preventing osteoporosis in immobilized (bedridden) patients can be considered from several perspectives:

Calcium intake is crucial for maintaining bone health and preventing osteoporosis, as established by various studies 2, 3, 4, 5, 6
However, the effectiveness of calcium supplementation in reducing fracture risk has been questioned, with some studies reporting only weak efficacy 3, 4
Additionally, calcium supplementation has been linked to potential adverse cardiovascular effects, as well as gastrointestinal side effects and the risk of kidney stones 2, 3, 4

Immobilized patients may be at higher risk of osteoporosis due to lack of mobility and weight-bearing activity
Calcium and vitamin D supplementation may be beneficial in preventing osteoporosis in these patients, particularly when combined with other treatments 5, 6
However, the potential risks and benefits of calcium supplementation must be carefully considered, taking into account individual patient factors such as age, gender, and ethnicity 2

Calcium supplementation should be prescribed and taken cautiously, accounting for individual patients' risks and benefits 2
The current Recommended Dietary Allowances for calcium appear to be a good target, with potential risks for chronic disease if intakes fall too short or greatly exceed these recommendations 3
Combined calcium and vitamin D supplementation is an essential component of the management of osteoporosis, particularly in patients with documented osteoporosis or those at high risk of calcium and/or vitamin D insufficiencies 6