What happens if diabetic ulcers don't heal? Is it a permanent open wound?

Bone infection. If wounds do not heal there is an increased risk of serious wound infection of soft tissues, gangrene, and bone, osteomyelitis.
Serious consequences. Most people call neuropathic ulcers on the soles of the feet / toes "diabetic ulcers." here, a permanent open wound can result. Much worse / more likely, bacteria will eventually get in through the ulcer and set up a deep infection. This can lead rapidly to amputation or even death. The keys are changing weight-bearing, wound care, avoiding nicotine, checking the circulation, and glucose control.
Should heal. A thorough workup, coupled with appropriate treatment and a knowledgable doc as well as a compliant patient should enable some form of closure for any wound eventually whether with standard therapies, or more advanced products with living cells, grafts, flaps, hyperbaric oxygen etc.
Diabetic ulcers. Good question. In my experience, weither the ulcers heal or they go on to require extensive surgery(amputation). Because the diabetic patient has a higher glycemia level, the serum is an excellent medium for bacteria to grow. This leads to infection and quite often, a disastrous outcome, requiring amputation of a digit, foot, or leg.
NO, needs care. Diabetic ulcers are usually from poor circulation and swelling in the lower extremities. Treatment is leg elevation, compression stockings to decrease swelling, and removal of the dead materials from the ulcer area. Typically this, plus use of platelet concentrates are effective in getting the skin to resurface the ulcer area, or grafted. Important to have it cared for regularly.
Wound care. . Diabetic ulcers will generally heal if you offload the area (decrease direct pressure with an insert, or a wheelchair), have your doctor trim the callus and dead tissue away on a regular basis, and if the ulcer is infected, you may need oral or IV antibiotics, depending on the severity of the infection. If it continues to progress, a conservative amputation may be necessary.
Amputation . See podiatrist. Get checked for pad and treated if needed. Control blood sugar. If not treated the ulcer can get infected and can lead to amputation.
They can heal. Diabetic wounds can heal, just need to find the underlying factors that are causing the wound not to close. Need to make sure that the pressure is relieved from the area. Eliminate any infection and make sure that proper nutrition is present to help with wound healing. Make sure that you are being seen by a podiatrist or a wound care center for your care.