We had a resident rat when we moved in here. Called in the council rat man which cost £50. He laid poison in all the places that were dog proof. He warned us that usually they leave the house in a desperate to find water and die off premises. If we were unlucky, the rat would crawl into a cavity and die there, in which case, success would be announced by a smell we'd have to put up with for a week.
We were lucky.