Infinity is a funny thing. In an infinite time period everything that can happen will happen. In theory, roads could not turn into water. But in an infinite universe they would eventually. So lets run with that.
It was a shock to find out that the roads had turned to water. While the populus were away in the land of nod the composition of the roads changed from asphalt to water. Upon waking some people noticed it right away, understandably confused. Some people had to look twice, and some people realised when they went to their cars and found out that they had sunk. Some people had to fall in before they realised the change.
Eventually the ducks, geese and other waterfowl moved out of the parks and took over the waterways. Aquatic plants started to grow and where road water met with streams, rivers and creeks fish quickly gained prominence. Amphibians also capitalised on this, with frogs, newts and toads advancing into the flooded streets. When the gushing streets come into contact with aquariums and zoo’s their aquatic inhabitants moved into the new excess of liquid. Seals and penguins congregated on concrete islands. Pods of whales started to replace traffic and dolphins leap from the reborn canals. Sharks created no swim zones, and cuttle fish, octopuses and squids gave rise to urban cephalopods, followed by crabs, shrimps and lobsters. In time reefs blossomed, joined by reef fishes. Even sea serpents have been sighted, although reports are awaiting confirmation.
Even human beings adapted. Over time, wooden bridges and platforms linked streets together and the cars they once had were replaced by boats, both motorized and paddled. Instead of blocks of houses there were islands and different communities became different tribes, all relying on the waterways for sustenance.
But in an infinite universe everything will happen and at some point, the roads will return to asphalt. But for the while the roads are waterways, filled with a wide variety of animal and plant life, and human beings who have become accustomed to an aquatic existence.