Can loose teeth be tightened?

Yes and no: Depends on the severity. Sometimes slight mobility can be corrected with periodontal treatment, splinting, bone grafting, etc. Unfortunately, if the mobility is more severe, there isn't much that can be done other than extraction. If there's inadequate bone to hold the teeth securely in the mouth, they're kinda out of luck.

Often, yes: If looseness is from biting too hard, easing the bite will allow the loose toot to tighten on its own. Balancing the bite can help. Teeth can also be splinted, or bite guards can be worn. If you've lost a lot of bone due to gum disease, mobility can be reduced, but probably not completely eliminated.

Possibly: Teeth are supported by ligaments that connect them to the jaw bone. If the amount of support has been compromised by disease loose teeth may result. If the disease is treated many times the ligaments can again support the teeth and give you the impression of "tight teeth". See your dentist to determine the cause of your problem.