Far from being inconceivable! It has been a huge issue for years. Before my mother passed away 2 years ago she was hospitalised many times and on each occasion she went down hill rapidly in hospital due to lack of nourishment, dehydration, infection etc. She had dementia and the hospitals hadn't the resources to provide basic care. Drinks were frequently left well out of reach, no one encouraged her to drink except ourselves when visiting. I went in one day well after lunchtime, her lunch (sandwiches in a sealed plastic pack) were totally out of her reach on a table.
On returning to the home they would get her built up again until the next time hospitalisation was necessary and the same would happen again.