Just before the fall, Mother's Milk of Extropia were developing a medichine variant that would be passed from mothers to offspring, which would save animal breeders and engineers significant amounts of money. They had created a successful prototype in a breeding population of smart rats, and were poised for full commercial release when the rats escaped during the chaos of the Fall. Mother's Milk went under, but their legacy remains.
Everlasting rats are smart. Rats can be smart to begin with, smart rats are genetically engineered to be even smarter, and their medichines mean that everlasting rats are immortal and never stop learning. An everlasting rat will know the habits and schedules of every transhuman in the area. They recognize types of robots and vehicles, avoiding them or hitching a ride. They exploit the fractured landscape of Extropia, simply shifting to a neighbor whenever one person or organization attempts pest control. The sophisticated games of hunting and evasion by everlasting rats and smart cats have inspired a children's story and a pamphlet on small-unit tactics.
Their medichines render everlasting rats virtually immune to poisons and toxins, and the enhanced healing means a full recovery from any non-mortal wound. Currently, the only way to control the population is with rat-oriented disassembler swarms (generally discouraged by worried neighbors), tailored nanoplagues (generally discouraged by everyone) and engineered predators, mainly smart cats, cheshires and small bearcats.
Everlasting rats are as smart rats, plus medichines.