My father has vascular dementia and is only swallowing liquids. We give him a meal supplement 4x a day. Is this unhealthy?

Have you spoken to a registered dietitian about this? Or his doctor?

How did you figure out that he needs 2000+ calories? Is he very active? Is he large man? I don't mean to imply that you are wrong, I'm just curious.

Isn't the key thing that given these severe restrictions your father still enjoys whatever he can manage? By all means take advice from a dietitian, and from any qualified professional you like; and you could try blending the occasional egg into other foods (apple amber springs to mind, if he likes applesauce); but I wouldn't beat yourself up in pursuit of perfection.

In a situation like that, it's all about the calories. My absent brother had a fit in the hospital when I said that mom doesn't eat that much so we give her nutritional drinks. He went on this rant about how it's just sugar milk and that she needs nutrition. What did the doctors suggest? That we give her nutritional drinks. What did the RN say? That her own mother will only eat nutritional drinks and peanut butter and she followed up with "It's about the calories". My brother shut up after that.

I fully expect there will be post from people talking about nutrition and rail against sugar. But when someone is in that state, it's all about the calories. You aren't prepping them for a marathon. You are simply trying to keep them alive. Many older people die not by some acute event, but they simply slowly starve themselves to death. It's called a death spiral. Once an older person starts losing weight it just keeps rolling along and for an older person it's hard to regain any lost weight.

By all means consult a doctor. But I don't think you are doing anything unhealthy at all. You are keeping your dad from starving. I would suggest you mix up with protein drinks. While they have less calories by volume than a nutritional drink, they are packed with protein. That will help mitigate muscle loss which is also a big problem with elderly people.

I do have a question. Where are you finding shakes that have 500 calories in 200ml? I'm assuming you meant to say ml instead of mg. I have never seen a nutritional drink with that many calories in such a small volume. The stuff I get is between 200-300 calories in 250ml.

Best bet, ask the doctor if he can do a dietician referral. Docs don't know all the details like a Registeted Dietician would.
 If dad can't be present at the appt., you could go and ask questions. Be sure to have his height, weight and age with you.

I'm assuming you mean the nutritional supplement like Ensure, Glucerna, Boost, etc.
is 200 ml instead of 200 mg. (ml stands for milliliter) 200 ml. would be about 6-2/3 ounces.

The only things I would check is if your dad is having loose stools or diarrhea from too much of the drink. It can cause that because there's oil in it. 

Also, if he's eating other liquid foods, he's getting quite a few calories. Actually too many for his age and activity level.
Most orders are for 1-2 "shakes" (supplements) a day. 

They also have vitamins in the supplements, so if he takes a vitamin pill or drops AND takes 4 shakes a day, he may be getting too many vitamins.

Does he have any problems with elevated blood sugar (diabetic)? If so, he can't be drinking regular supplements. They would have to be made with artificial sweeteners.

Schedule an appt. with a dietician. You'll learn a lot.