How did Fenton survive more than 7 days without food in the basement?

Yes. The normal adult can last a month or more without food as long as you have water. Without water, it's close to a week or less. A comatose adult would last 2 weeks without both.

Children don't fair as good due to lower fat storage. But even then, a 1 year old lasted six days and a 2 year old was in critical condition at nine days. https://www.thesun.co.uk/news/2352824/mum-leaves-toddler-starve-to-death-leaves-nine-day-jaunt-lover/

Fenton could easily last a week. Plus we don't know if he had any access to food or water, we are not explicitly told. His dad or brother could have brought food or there was a sink or something.

Andreas Mihavecz, an 18-year-old Austrian man, may have survived the longest without drinking water: Police accidentally left him in a holding cell for 18 days in 1979. It's a fuzzy record, though, since he allegedly licked condensation off the walls of the prison.

http://www.sciencealert.com/here-s-the-longest-people-have-survived-without-air-food-water-sunshine-or-sleep1

Thus it is possible, but hardly guaranteed that Fenton might have been able to survive for a week locked up and possibly without any food or water.