Sometimes dementia or Alzheimer's disease descend quickly and unexpectedly, and in the flurry of health-care related decisions that follow, the question of who inherits what is forgotten or considered too trivial to address. In this case, how do you ask somebody who is non compos mentis ("not of sound mind") for a beloved heirloom?
Even extremely forgetful people have moments of lucidity. Sometimes those moments tend to occur at a certain time of day. Try to choose one of those moments to pose your question, and when you do, bring along another family member who can bear witness to the answer. Even better, bring a family member and a recording device to have an objective record of your conversation. Pose the question gently, and try not to get frustrated if the conversation doesn't go the way you'd hoped.
It's extremely important not to trick your relative into giving you the answer you want. Besides the fact that it's unethical to take advantage of a person in this state, it will also create bitterness within your family.
In the end, it may be up to you and your family to make those decisions about inheritance after all. And, when all is said and done, if you don't get the beloved object that you wanted, keep in mind that you still have your memories of your relative, and those are most valuable heirlooms of all.