Are you sure? Most often in this situation the shake drinks that are supplied are something like Fortisip - which are also used when patients can't manage solid foods for whatever reason.

Fortisip is not only vitamins and minerals, but has a high protein and calorie content (about 300 calories per 200ml drink). It is also gluten and lactose free so that lactose intolerant and coeliacs can have it. Fortisip is designed to be a complete food, in that you can actually live and be well nourished having it and nothing else, so long as you take in enough to have sufficient calories.

If the decline in weight is solely due to not eating and there's no underlying cause for lack of appetite then it is down to just getting in as many calories as you can, any way that you can. Forget about balanced diets and "healthy" food, if someone is starving then calories take priority over everything.

Many, many people with dementia develop a sweet tooth - even if they hated sweet things before. This can be an advantage because you can get them to eat calorie-dense foods. Also in the elderly the tastebuds that sense bitterness are the last to fail, which means all foods can taste bitter - which is why the elderly all tend to have sweet tooth anyway

What you can try:

Sweet things, of any sort, biscuits, cakes, sweets, chocolate, puddings
Always use sugar, never sweeteners
Full fat milk or cream, custards etc, not "healthy" versions
Offer in small amounts as large plates of food can intimidate
Finger food in case there are issues with cuttlery
Leave biscuits and sweets in plain sight so that they can be nibbled
Try some high-calories savouries like cheese if it's acceptable
Don't present food choices as in "what would you like for lunch?". People with dementia can find it hard to deal with choices. It is better to say "we are having xxx for lunch today, that will be nice"

Has there been an assessment by a SALT? There could be a swallowing issue and perhaps even choking incidents leading to a reluctance to eat.

Sadly in advanced stages dementia can mean that people forget to eat, do not know what hunger means or even not know what to do with food when it is placed in their mouths.