I've been through it all by now. I've seen 7 of my rats pass over the past couple of years and only 1 has died at home naturally.
I find that they do let you know usually. When a rat gets to the point where they will refuse food or they start to lose a signifant amount of weight due to a lack of eating, they're usually very sick. Even when a rat is feeling a little under the weather, they will usually take something yummy from you, even if they only eat a little.
When a rat is dying of old age, you can usually tell when it's time as well. When they get to the point where they can no longer walk without having to really pull themselves along or they are even falling down often then you can tell that they are slowing down. Pay attention to their breathing and the amount that they're eating. If a rat is just old it may just pass in it's sleep... if you ever notice that it's really starting to struggle with it's breathing then you may want to take it to the vet and see if it's in it's best interest to put him to sleep.
As for the rat with the tumors.... Sometimes rats can live a long time with a tumor(s). I had a 2 year old rat with cancer. She had multiple tumors and her largest one was on her rear and about the size of a kiwi fruit. She still ate and played a little bit but I could tell that she was starting to get overcome with the cancer. A new lump was turning up almost weekly and she was very ill. She started to get a wheeze so it was safe to assume that it was starting to reach her lungs as well. Within a week of the wheeze settling in she started to eat at her tumor.
I picked her up and held her close to my face. I could hear her breathing and she was very calm. This was not normal for her. I took that and the eaten tumor as a sign that she was ready to go.
Sometimes a tumor will grow so large that the rat can no longer be mobile or groom itself. This is when it starts to become a problem. Depending on where the tumor is it might be ok for a while.
Another good tip that I was told by my breeder (who is also a vet tech) is that when an animal or rat is cold to the touch for a day or two that it's a pretty sure sign that it's little body is starting to shut down and he/she can no longer control their body temperature.
I hope some of these things help you out a little. I'm sorry to hear that you're having a hard time right now. Losing a pet is never easy. Rats are the greatest and their lives are too short. Always remember that not all rats live to be 2 years old. By the time that a rat reaches a year, it is around mid-life or even a little more. No matter how young or old, they will be missed when they pass. They always give more to you in their short lives than you are losing when they are no longer with you in a physical form.
Take care.
