Father has stopped eating. Should I continue to encourage food?

My dad has stopped eating in the past few weeks and even drinking at one point. We put an IV in him and he pulled it out, but tried again and were successful. He is not dehydrated but is 110 pounds as of today. He has lost 40 pounds in the past few months. He was diagnosed with dementia a few months ago and everything has gone downhill. He lives in a nursing home. He's 66 years old. He suffered a really bad brain injury from a fall 2 years ago, was in a coma for 2 months, then finally woke up so a lot has happened. Should I continue to encourage food?