How do I respond to someone with dementia who is losing their memory?

What you really want is for them to be happy, so minimizing their upset by not correcting them may be the way to go. If you see they're happy thinking their dead loved one came to lunch, then ask, "Oh yeah? What did you have for lunch," or "what did you guys talk about?"

The gold standard for Alzheimer's care is that if the person is talking about something that doesn't make sense, it's ok, just ask them questions to keep them in the conversation because it's a way to engage them. How can you give them opportunities for them to be confident and correct because they are living in a world where more and more the things they say and think aren't correct. They're watching reactions and they can tell when they say something that's off, but they don't always know how to react, so they watch carefully. If you need to go to the bathroom and have a cry or laugh or get out emotion, go do that, but out of their range.

If they're asking for people who are dead, pay attention to how long their short term memory is so you can figure out a realistic goal, like, "Oh he went up to the mountains for the weekend, but you know he'd be here if he were around." You can even leave written notes from the person. But you have to prepare in advance for these moments.