Will a hospital release a patient to get home by themselves if their not able to care for themselves?

No. A primary criteria for hospital discharge is safety. If a person does not have a safe place and the ability or resources to provide basic life needs, the safety criteria is not met. Hospitals are closely monitored to assure they are meeting established standards of treatment and safety. Most hospitals have case managers to assure patients are discharged to a safe environment.
Hospital dischage. Unfortunately patients sometimes get discharged to unsafe situations, family members and friends has to step up and help when a patient does not qualify for a nursing home or home health. Sometimes people have to pay for private health givers. It is not always an ideal situation esp. If family members do not want to step up.
No. The short answer is no, but the longer answer is it depends on what you mean by "care for themselves". If the patient can do basic activities of daily living, and is competent to make decisions, sometimes the patient may be discharged when medically stable, although some observers would wish that the patient would choose to go to an inpatient rehabilitation facility.
Sometimes. Unfortunately there are times when patients themselves choose to return to unsafe living conditions, often against medical advice. If they are able to make comptetant decisions, that can still make bad ones and there is not much that hcp can do.
Yes. Happens often enough. No longer meet inpatient criteria but have no insurance. No snf will touch them.
No. The social workers make necessary arrangements to get help- home health, sitters or nursing home placement if applicable.
It depends... In general, a hospital is required to ensure a safe discharge plan for each patient, which would include either being able to care for themselves, or be discharged to a setting where the needed care would be provided. However, if a patient is competent to understand that their discharge may not be safe, a hospital may not hold a patient against their will, and must allow the patient to leave.
Usually No. Doctors work with social workers and therapist to evaluate whether a patient, their family, or friends have adequate resources (physical, emotional, financial, etc) to care for themselves. If they are not able to do so, they can still be discharged to a facility (nursing home, rehab facility, etc.) or to a friend/ relative’s home. Sometimes, however, patients and hospital staff disagree.
Typically not. However, it depends on the social situation the patient is in. If it is a fracture and his caregivers at home are able to assist him effectively, he may be released. If his home situation precludes effective home care, then typically such a patient will be released to a nursing home or an extended care facility where he can be rehab'd to the point of being able to care for himself at home.
No they will not. There is a safe discharge planning before any discharge from the hospital. This plan is made by the doctor, case manager, social worker, and other parties if needed like physical and occupational therapies. If a patient is deemed unsafe to be discharged for any reason like inability to care for themselves then a plan will be made to make the discharge safe, for instance, arranging for home care.