HELP! Is my sister's cat dying? Here are the symptoms....?

My sister, niece and her cat moved in with my husband and I about a year and a half ago. I also have a cat, whom I've had for 11 years. He's super healthy.

My sister's cat WAS healthy up until recently.

Here's the symptoms:

1) He's been hiding out-he's been under my sister's bed for 2 days. She went and pulled him out a couple of times, and brought him to his food and water bowls, but he didn't eat anything, and my sister had to pick him up and carry him back to her room.

2) He's moving SUPER slow...he's always been a bit of a slow cat, but now it's pretty bad. He seems to have little to no energy

3) He won't eat or drink-my sister always fed him hard food, and he stopped eating that a few weeks ago. She thought he didn't like the brand or flavor-she has since tried about 5 different hard foods-he wouldn't eat that, so she got wet food-again, no luck. I don't know for sure when the last time he ate or drank was.

4) He's lost weight. I hadn't seen him in a couple of days, and when I saw him today I was shocked. He looks sunken in. You can see and feel every knob in his spine, his shoulder blades, etc

5) My cat (who has gotten along wonderfully with my sister's cat) has been randomly going up to her cat and sniffing him for long periods of time.

6) My sister's cat seemed ok a few days ago-he even chased after a moth a few nights ago.

7) He's still purring when you pet him

8) He's always very vocal, that doesn't seem to have changed

9) His eyes still look very bright and clear

10) His nose is dry

Oh, and some background-my sister adopted him from a shelter 11 years ago. They estimated his age at the time of the adoption was 4-5 years old, so that would make him 15-16 years old now.

Does this sound like he may be dying?

I know all cats and situations are different, but I'm just trying to get an idea of what might be going on. My sister is trying to get an appointment at a local animal hospital right now. If he is suffering, she will do what's best for him.

Also, again, I know there is no one answer but I'm wondering if maybe anyone could give me an estimation on how much time he might have from this state to his death?

Thanks in advance for your help, advice and kindness!